From e8a3c3d4ad46b2b5fa02a83d8f13c01c6327092c Mon Sep 17 00:00:00 2001
From: Robert Lanzafame <R.C.Lanzafame@tudelft.nl>
Date: Wed, 13 Nov 2024 14:00:24 +0100
Subject: [PATCH] WS 2.1 final
---
content/Week_2_1/WS_2_1_solution.ipynb | 85 +-
.../students/Week_2_1/WS_2_1_solution.html | 751 ++++++++++++++++--
2 files changed, 709 insertions(+), 127 deletions(-)
rename content/Week_2_1/WS_2_1_wiggle.html => src/students/Week_2_1/WS_2_1_solution.html (85%)
diff --git a/content/Week_2_1/WS_2_1_solution.ipynb b/content/Week_2_1/WS_2_1_solution.ipynb
index 4118fe0b..f238aefb 100644
--- a/content/Week_2_1/WS_2_1_solution.ipynb
+++ b/content/Week_2_1/WS_2_1_solution.ipynb
@@ -40,66 +40,27 @@
"id": "0bbcc9be-71bc-4bb3-b665-58c64339747d",
"metadata": {},
"source": [
+ "1. This is in general how the code works: you should have seen that for each case, once you define the Python variables, there are ready-made functions to complete the analysis: first by running the simulation (`run_simulation_1D`) which initializes the volumes (`initialize_1D`) then sets up the time (the loop over `t`) and space integration (`advection_1D`). Then you can plot the initial condition (`plot_1D`) and visualize each time step (`plot_1D_all`). \n",
+ "2. Applying the cyclic boundary condition is very simple: you only need to shift the indexing from the \"math\" in the textbook by 1 when implementing in Python. This does introduce a slight error since you are actually calculating $phi$ for a volume to the left of your index; however, for small volumes it is negligible (and you could shift it back in each time step, if you wanted). \n",
+ "3. Note also that the cyclic boundary does not have any mathematical basis, and is not modelling \"reality\" in any way. It is a convenient \"trick\" that we use to make it easy to observe how the wave moves in space without worrying about the particular location of the wave (x) at any time.\n",
"\n",
- "1. The wording in the assignment said something like \"apply central difference and forward Euler,\" but the textbook already derived the central (space) and forward Euler (time) schemes, so all you had to do was implement the discretized equation for $phi_i^{n+1}$ in the code.\n",
- "2. You should remove the `pass` from the code after adding your solution, as this is a way to \"do nothing\" in that part of the if statement, so it could lead to problems.\n",
- "3. Some of you accidentally used `p[i]` for the first term in the central scheme, which actually made it backward \n",
- "4. Task 1.1 was important: you should have seen that for each case, once you define the Python variables, there are ready-made functions to complete the analysis: first by running the simulation (`run_simulation_1D`) which initializes the volumes (`initialize_1D`) then sets up the time (the loop over `t`) and space integration (`advection_1D`). Then you can plot the initial condition (`plot_1D`) and visualize each time step (`plot_1D_all`). \n",
- "5. Applying the cyclic boundary condition is very simple: you only need to shift the indexing from the \"math\" in the textbook by 1 when implementing in Python. This does introduce a slight error since you are actually calculating $phi$ for a volume to the left of your index; however, for small volumes it is negligible (and you could shift it back in each time step, if you wanted). \n",
+ "Key things to notice about the activities in this assignment: \n",
"\n",
+ "1. In Part 1, we see that the central scheme is _very_ unstable (default settings). \n",
+ "2. In Part 2: making the initial condition smooth helps...for a short time (set `square=False`).\n",
+ "3. In Part 3: upwinding becomes (conditionally) stable; if CFL<1.0, you will see false diffusion.\n",
+ "4. In Part 4: we use the CFL number to confirm stability regions. Note that if you use a CFL of 0.8 and your solution is unstable, you implemented the upwinding scheme incorrectly. Check the tips above about the cyclic indexing to help solve your issue; note also that regardless of if or how you implemented the cyclic boundary condition, if you are using points that are to the \"right\" of the index for `p_new` then you did not implement upwinding correctly (for example, if you compute `p_new[i]` and the calculation includes a point `p[i + 1]`).\n",
"\n",
- "Key things to notice: \n",
+ "The reason we notice the above points is because our PDE is convection (hyperbolic) and our pulse is moving to the right, which implies that the upwind cells (volumes) are more important (they have a larger weight). Even though backward difference (the upwind scheme) is a lower-accuracy method (first order) than central averaging (second order), it is more stable.\n",
"\n",
- "1. In Task 1, we see that the central scheme is _very_ unstable (default settings). \n",
- "2. In Task 2: making the initial condition smooth helps...for a short time (set `square=False`). \n",
- "3. In Task 3: backward difference is stable (set `central=False`). \n",
- "4. In Task 4 and 5 we use the CFL number to confirm that it can help us design the discretization scheme (i.e., increments in space and time) to produce a stable numerical result.\n",
- "\n",
- "This is because the discontinuity is difficult to handle with the advection situation: the pulse is moving to the right, which causes large fluctuations as the discontinuity passes through the various volumes. Even though backward difference is a lower-accuracy method than central difference (second order), it is more stable. In fact, only a first-order method is needed to solve the linear advection problem (we set up central difference to illustrate the instability, as well as to prepare ourselves for solving the diffusion term).\n",
+ "It is important to recognize **three types of numerical issues** that are present in this assignment:\n",
+ "1. Instability caused by the nature of the PDE (a hyperbolic equation), combined with the numerical scheme (central averaging in space and forward Euler in time).\n",
+ "2. Instability as described by the CFL criterion.\n",
+ "3. Numerical diffusion (false diffusion), which is inherent in upwind schemes (an explanation is outside of the scope of MUDE: we are happy as long as you recognize this can be an issue!).\n",
"\n",
"_After the general comments here, the solution has been implemented in the code below. There is also a large section of code that facilitates the use of dictionaries to keep track of analysis cases; it's not part of the MUDE exam material, but you might find it useful when working on your projects, especially if you are working on a situation when you would like to evaluate a lot of scenarios and keep track of the input parameters. For example, you can see that each dictionary stores the variable values and a name describing it._"
]
},
- {
- "cell_type": "markdown",
- "id": "2efdf0cf-13ca-4837-9132-a1fdaec573b8",
- "metadata": {},
- "source": [
- "## Video Explanation\n",
- "\n",
- "**A video explanation for this notebook is available.** Watch the video directly [on YouTube here](https://youtu.be/IMSIVDfXi78), or run the code cell below to view it in your Jupyter environment."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "id": "cdc8695d-6c5f-4be7-ac49-1aa29fac0128",
- "metadata": {
- "tags": []
- },
- "outputs": [
- {
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- "<iframe width=\"800\" height=\"450\"\n",
- " src=\"https://www.youtube.com/embed/IMSIVDfXi78?si=slzMThsNcMU6vISG\"\n",
- "</iframe>\n"
- ],
- "text/plain": [
- "<IPython.core.display.HTML object>"
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- "source": [
- "%%HTML\n",
- "<iframe width=\"800\" height=\"450\"\n",
- " src=\"https://www.youtube.com/embed/IMSIVDfXi78?si=slzMThsNcMU6vISG\"\n",
- "</iframe>"
- ]
- },
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@@ -202,7 +163,7 @@
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"id": "b1465443",
"metadata": {},
"outputs": [],
@@ -240,7 +201,7 @@
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@@ -375,7 +336,7 @@
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@@ -421,7 +382,7 @@
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"id": "6f7306d6-c303-4cfb-bd24-2eb2976b695c",
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"outputs": [],
@@ -456,7 +417,7 @@
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@@ -512,7 +473,7 @@
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@@ -542,7 +503,7 @@
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@@ -582,7 +543,7 @@
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@@ -590,7 +551,7 @@
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GQAlAxKusJqMEIDAESgAiXoVbRqlKpmk2szcANCJQAhDxXDNKVbV1Kq2oCeJoAIQTAiUAEc+1mFti+g1A6xEoAYh4lS7tASQKugG0HoESgIhHRglAoAiUAEQ81/YAEhklAK1HoAQg4lU0FHOnOWMlkVEC0HoESgAinpVR6t0lSRIZJQCtR6AEIOJZNUq9uyRKqu+lBACtQaAEIOJZD8W1MkpMvQForZAKlObNm6eRI0cqNTVVPXr00OWXX64dO3Y0+5m1a9fKMAyP11dffdVJowYQ6jwzSgRKAFonpAKldevW6bbbbtOmTZu0evVq1dTUaMKECSovL2/xszt27FBRUZH9GjhwYCeMGEA4sDpzuwZKPMYEQGvEBnsArt5++2239y+++KJ69OihrVu3auzYsc1+tkePHjruuOM6cHQAwpX1rLdex9UHStW1pkqOVeu4pPhgDgtAGAipjFJTJSUlkqTjjz++xX2HDx+uzMxMjR8/XmvWrPG5X2VlpUpLS91eACJbpd0eII4WAQD8ErKBkmmaysvL09lnn63Bgwf73C8zM1MvvPCC8vPztWzZMmVnZ2v8+PF67733vO4/b948paen268+ffp01CkACAGmadrtAZxxMeqemiBJOkidEoBWCKmpN1e33367Pv30U23YsKHZ/bKzs5WdnW2/z83N1d69e/Xoo496na6bM2eO8vLy7PelpaUES0AEq641VddQjpQQ61C3lAR9e7CcFgEAWiUkM0ozZ87UihUrtGbNGvXu3dvvz48aNUo7d+70+rWEhASlpaW5vQBELtfHlyS4ZpSYegPQCiGVUTJNUzNnztTy5cu1du1aZWVlBXScgoICZWZmtvPoAIQj1wfiJsTGqFtKfaBEiwAArRFSgdJtt92mV155RW+88YZSU1O1f/9+SVJ6eroSE+tXq8yZM0f79u3Tyy+/LEl68skn1b9/fw0aNEhVVVX685//rPz8fOXn5wftPACEDqvZZHxsjAzDIKMEwC8hFSg9//zzkqRzzjnHbfuLL76o6dOnS5KKiopUWFhof62qqkqzZs3Svn37lJiYqEGDBunNN9/UpEmTOmvYAEKYlVFKiK2vNOhORgmAH0IqUGpNA7glS5a4vZ89e7Zmz57dQSMCEO6s1gDOOIckqVtqfe8kMkoAWiMki7kBoL1YzSYbM0pOSWSUALQOgRKAiGZllKxAycooHTpSpbo6HmMCoHkESgAiWmOzyfqpt67J9TVKNXWmDh+rDtq4AIQHAiUAEa2iSUYpPjZGxyXFSWL6DUDLCJQARLRKu0bJYW+zeilR0A2gJQRKACKa1R7AGdf4644WAQBai0AJQERr7KPkklGi6SSAViJQAhDRKhs6cyd4ySgdJKMEoAUESgAimj315pZRqm8RUFxWFZQxAQgfBEoAIpq3jFI3MkoAWolACUBEq2jyrDdJ9oNxi6lRAtACAiUAEc3KKFkNJyVqlAC0HoESgIhW2UxG6V/lPMYEQPMIlABEtIpqz4aTxyfXF3PX1pn691EKugH4RqAEIKJ5azgZ54hRl4bHmDD9BqA5BEoAIpq3hpOSa0E3GSUAvhEoAYhoFV7aA0iuLQIqOn1MAMIHgRKAiEZGCUBbECgBiGiVNS1llKhRAuAbgRKAiFZR7dkeQGoMlL78vlRFJcc6fVwAwgOBEoCIZmWUXBtOStI/i49IktZ/U6yz5r+rpZsLO31sAEIfgRKAiFbpJaNUVHJMr239zn5fZ0pzl31GZgmABwIlABHNW8PJXcXlMps05K41Te0uPtqZQwMQBgiUAEQ0bw0ns7olK8Zw389hGOrfLakzhwYgDBAoAYhYpml6bQ+QmZ6oWROy7fcOw9DDVwxWZnpip48RQGgjUAIQsawgSfJsD/DTnN6SJEPS+v86R5NH9u3MoQEIEwRKACKWW6DUpD2AlWEyJXVPdXbmsACEEQIlABHLag1gGFK8o0mg5JJhsgq+AaApAiUAYa2o5Jg++LbY69J+19YAhuFeve2aYXLNPAGAq9hgDwAAArV0c6HmLNuuOlOKMaR5VwxxqzWyH1/S5DlvkmQYhuJjY1RVU0egBMAnMkoAwlJRyTE7SJK8N420Hl/ijPP+q87KKjH1BsAXAiUAYWlXcbkdJFmaNo301hrAlfVYE2uKDgCaIlACEJayuiWrSc9Ij6aRlXZX7uYzStYUHQA0RaAEICxlpidqwmkZ9vsYQx5NIxu7cnvPKDVOvZFRAuAdxdwAwlaCSwD04vSRGpfdw+3rjcXc3v8mtKfeyCgB8IGMEoCw9fUPZfa/vWWNrExR067clsapNzJKALwjUAIQlmpq6/TPg+X2+yOVNR77WJkip49ibqvIm1VvAHwhUAIQlvb866iqahszQWUV3gKl5jNKVtsAMkoAfCFQAhCWdrpMu0lSmZeMUkW174aTrtsJlAD4QqAEICx9/cMRt/dHvGWUWmo4aWWUmHoD4AOBEoCwZBVyO2Lquykdqaz22KfFhpNklAC0gEAJQFiyAqVTM1Mlec8oVbTUcJKMEoAWECgBCDvVtXXaVVy/4i2nbxdJLRVzt9BwkowSAB8IlACEnd3F5aquNZUc79DJPeszSt6KuVtqOGkXc5NRAuADgRKAsGMVcp+UkapUZ5wkX1NvVo0S7QEABIZACUDYseqTTu6RotSE+icxNdtw0ufUG8XcAJpHoAQg7Ow80BAoZaQqxdlcoNR8Rskq5qYzNwBfCJQAhB1r6u3knqlKacgolVV4tgewV735yCjRHgBAS2KDPQAA8EdlTa12N6x4OzkjRbV1pqTmV705W2oPUENGCYB3ZJQAhJVdxeWqqTOVmhCrnmlOpSbUF3NX1tSpqklmyOrM3WJ7gGoySgC8I1ACEFasabeBGSkyDEPJCY1BUHmTOqWKltoDxFlTb2SUAHgXUoHSvHnzNHLkSKWmpqpHjx66/PLLtWPHjhY/t27dOuXk5MjpdGrAgAFauHBhJ4wWQEcqKjmmD74tVlHJMbft1sNwT86o758U64hRYkPA03T6rfFZb81nlCrJKAHwIaQCpXXr1um2227Tpk2btHr1atXU1GjChAkqLy/3+Zldu3Zp0qRJGjNmjAoKCjR37lzdcccdys/P78SRA955u9m357aOPn6wti3dXKiz5r+rn//hQ501/10t3Vxo72u1BhjYEChJsle+lTV53luLq94airkryCgB8CGkirnffvttt/cvvviievTooa1bt2rs2LFeP7Nw4UL17dtXTz75pCTp1FNP1ZYtW/Too4/qyiuv7OghA7aikmPaVVyurG7JykxP1NLNhZqzbLvqTCnGkOZdMUSS2m3bT4afoOUF+zrs+O297bc/GSLTNPWr1z/zuZ9hSOOze+j/vjpg//9aZ0pzl32msSd3V2Z6onZaK94yUux9Up2xOlhW6dF0srKFZ73ZDSfJKAHwwTBN0wz2IHz55ptvNHDgQG3fvl2DBw/2us/YsWM1fPhwPfXUU/a25cuX6+qrr9bRo0cVFxfntn9lZaUqKyvt96WlperTp49KSkqUlpbWMSeCiNc0KJowqKfe/mx/sIcVUV69aZSG9z1Op/36bdWZ0odzxysjzSlJuuyZDfrkuxItmjZC40/NsD9z8j1vqaq2Th/c/WP1Oi7R45jfHDii8x5fp/TEOH1y34ROOxcAbVdaWqr09PQOv3/7lVFasWKF39/g/PPPV2Ki5y+olpimqby8PJ199tk+gyRJ2r9/vzIyMty2ZWRkqKamRsXFxcrMzHT72rx583T//ff7PR7Al6KSY3aQJNVnQAiS2pdhSP27JemfB8tVZ0ppzlj1SE2wv+6t6WRdnamq2pam3mg4CaB5fgVKl19+uV8HNwxDO3fu1IABA/z6nCTdfvvt+vTTT7Vhw4ZWfR9XVpKs6XZJmjNnjvLy8uz3VkYJCNS3B8rtIKk5RsP/uOZw27Kto48frG0Ow9Dsidn63Vs7VNvwhRgZKi6r0rcH66fdsnumul3fVtPJUpepN9cmkj4bTsY1Npw0TdPr7wwA0c3vYu79+/errq6uVa+kpKSABjVz5kytWLFCa9asUe/evZvdt2fPntq/3/2v9wMHDig2NlZdu3b12D8hIUFpaWluL6At1u444LHNYRiaM+kUORpuvA7D0Pwrh2j+FUPabduVZ5zQoccP1raHrxism8eeqA13n6tXbzpTYwZ2U61p6rZXPtbWPf+W5F7ILUkpCZ4PxnVd8t9Sw0lJdvYJAFz5lVGaNm2aX9NoU6ZM8SsQMU1TM2fO1PLly7V27VplZWW1+Jnc3Fz9/e9/d9u2atUqjRgxwqM+CWhvH3xTrEXv75JUPz1kmo03+8kj++rSYb20u/io+ndLUmZ6/bUz9uTu7bZt1gXZHXr8YG7LTE9UZnqiTstM10W/X6/Cfx3VnzbtkSRluEy7SfXF3JJ0xGXVm5VRcsQYinU0P/Um1TedtFbBAYAlpIq5b731Vr3yyit64403lJ2dbW9PT0+3A7Q5c+Zo3759evnllyXVtwcYPHiwbr75Zt10003auHGjZsyYoVdffbVVq946qxgMkedAWYUmPbVBxUcqNXlEH915/kCPmz3ax7a9h3Xlc++rtuG3lWFI868Yoskj+0qSHlu1Q79/9xtNy+2n+y+rr2ksPHRUYxesUVK8Q188cKHX45qmqQFzV8o0pY/uGa8eqc5OOR8AbddZ9+926aP08ccfq6qqqs3Hef7551VSUqJzzjlHmZmZ9mvp0qX2PkVFRSosbOypkpWVpZUrV2rt2rU6/fTT9eCDD+rpp5+mNQA61Hf/Pqrpizer+EilsjNS9ZtLBykzPVG5J3YlSOoAGWkJbnVgZkPLAKvvkv1gXJdibqs3kq9mk1J9HSNNJwE0p136KI0cOVJffvmlTj755DYdpzXJrSVLlnhsGzdunD7++OM2fW+gtZZuLtTd+dtl/dd68dBMJcYzZdORdhWXq+lvh1rT1O7io8pMT2xsOOlao1Td/Io3S0KsQxXVdTzGBIBX7ZJRCqHZO6BDWa0AXP+Lf/L/dno8ZgPtK6tbsmKaLEhzGIb6d6tfMGJllLwVc7cUKFlNJ3kwLgBvQuoRJkCo21Xs2QrAymyg42SmJ2qel9Vx1jRnmrNh1Zvr1FsLz3mzWAXcru0EAMASUo8wAUJdVrdkGZJbRsk1s4GOM3lkX6+r4yTvDSdbm1FqrFFi6g2AJwIlwA+Z6Yka0D1Z3x6sf1Bz08wGOpbVMqApu5jbS8PJlpb8uzadBICmCJQAP5Ucq78ZP3j5YJ13ag+CpBDQGCg19lGyHkvi2lTSGzujRDE3AC8IlAA//Lu8SsVH6h+qfMXwE5ScwCUUCqyGk5U1daqqqVN8bEyrM0oJFHMDaAbF3IAfvv6hTJLUu0siQVIISXH5WZQ31ClVtjKj5LSLuckoAfDULoHSfffdp27durXHoYCQ9vWB+oeyntzkWWMIrlhHjBIbao2sgu6KhoySs5UZJWqUAHjTLn8S33fffe1xGCDk7WzIKA3MSAnySNBUijNWx6pr7YJuu+FkizVK9YFUBaveAHjB1Bvghx376wOlk3uQUQo1qU0Kuv1tOMkjTAB441eg9Omnn6qurvW/TD7//HPV1NS0vCMQJnYy9RaymvZSouEkgPbgV6A0fPhwHTp0qNX75+bmuj3AFghnxUcq9a/yKhmGdFIPpt5CTWqTQMnfhpNMvQHwxq8aJdM0de+99yopqXVdiKuqqgIaFBCKrBVvfbok8RDcENS06WTr2wOQUQLgm1+B0tixY7Vjx45W75+bm6vERJrxITLs/MGadiObFIpSEuqf92YFSlaGyEnDSQBt4FegtHbt2g4aBhD6vrZXvFGfFIoap96sYu5WZpRiaTgJwDdWvQGtZGWUsgmUQpIdKHlMvbW06o2GkwB8I1ACWsE0TX19gB5KocyuUapsOvXWuowSNUoAvCFQAlrh4JFKHT5arRhDOrE7gVIoSgkwo2QVc7PqDYA3BEpAK1jTbv26JreYoUBweKx6a/Wz3sgoAfDNr0BpypQpOnbsmCRp7969HTIgIBTZhdz0TwpZnn2UWtlw0qpRopgbgBd+rXpLSUlRZWWlEhMT1a9fP3Xp0kXDhg3TsGHDdPrpp2vYsGEaNGiQ4uLiOmq8QFBYgRIduUNXqrP+944dKFX72XCSYm4AXvgVKC1cuND+965du7Rt2zZ98skn2rZtm1asWKHdu3crNjZWp5xyij755JN2HywQLF83TL1RyB26Am046SSjBKAZfgVKrvr166d+/frpsssus7eVlZVp27Zt+vTTT9tlcEAoME2TjFIYsAIlzz5KrW04SaAEwFPAgZI3qampGjNmjMaMGdOehwWC6ofSSpVV1MgRY2hA9+RgDwc+WDVKFdV1qq6t8789AKveAHgRcKC0efNm3X333Tp48KBOOukknX766farb9++7TlGIKisbFK/rkktTuMgeJITGn+dHT5arZo6U5I/DSfJKAHwFHB7gKlTp8rhcGjGjBkaMGCA1q1bp+uuu079+/dX165d23OMQFBZgRIduUNbnCNGiQ1Bz7/KGx/I3VJ7ACuQqqqtU11DcAUAloAzSnv37tWbb76pE0880W37nj17tG3btraOCwgZO+1CbgKlUJfijNWx6loVH6m0t7X4rDeXqbnKmjolxpM1BNAo4IzSWWed5bWXUtMCbyDcffZ9iSSpe2p8kEeClqQ2TL9ZgVKcw5Ajxmj2M06XqTme9wagKb8ySpdddpndN2nGjBl64IEHNGTIEKbaELH++lGhPv++VJJ03xufK94Ro8kjqcELVdZjTIqP1E+9taamLNYRI0eModo6kzolAB78CpQGDhyoDz74QM8//7wOHTokScrOztZll12m3NxcDR8+XEOGDFF8PH95I/wVlRzT3OXb7fd1pjR32Wcae3J3ZaYnBnFk8CWlSUbJ2UJ9kiUhNkZHq2p53hsAD34FSo8++qj97++++07btm2zX/Pnz9euXbvkcDh0yimn0EsJYW9Xcbma1vbWmqZ2Fx8lUApRVouAQw2BUmtXKTrjHDpaVUtGCYCHgIu5e/furd69e2v48OGSpBNOOEFHjhxRQUEBQRIiQla3ZBmSXGMlh2Gof7ekYA0JLUhJqH+MySF76q31GSWJ7twAPAVczP3+++8rKytLffv2Vd++fZWRkaEHH3xQw4YN02233daeYwSCIjM9UVeN6G2/dxiGHr5iMNmkEJbqdJ96S2ih2aSF570B8CXgQOnmm2/WoEGDtHnzZn366adasGCB/vGPfygnJ0fFxcXtOUYgaAafkC5JOjOrizbcfS6F3CGusUbJv4wSz3sD4EvAgdK3336rJ554QmeccYYGDRqka6+9Vps3b9bpp5+uO+64oz3HCASN9YDVfl2TySSFAWvV20G7RsnPqTcySgCaCDhQOvXUU7V//363bYZh6IEHHtDf//73Ng8MCAVWoGTVviC0WVNvVQ1F2S09581iFX1XkFEC0ETAgdL06dP1i1/8QoWFhW7bS0pKlJ6e3uaBAaHAehK9lalAaEtJcP85tTqjFEdGCYB3Af/2v/POOyVJJ598sq644gqdfvrpqq2t1Z///GctWLCgvcYHBNWRhoxSGoFSWEht8nNqfTE3D8YF4F3Av/3379+vgoICffLJJ9q2bZuWLFminTt3yjAMzZ8/X2+++aaGDh2qoUOH6sILL2zPMQOd5kilNfVGoBQOmk6ROv3NKNFwEkATAf/279Gjhy644AJdcMEF9raKigpt375d27Zt0yeffKIVK1bo4Ycf1uHDh9tjrECnK7VqlMgohQWPqbdWduZ2WjVKZJQANNGuv/2dTqdGjhypkSNHtudhgaA5UkFGKZx4TL21sjN3Y0aJQAmAu4CLuYFoYE29Nb0BIzQ1/Tn586w3iWJuAJ4IlIBmNAZKtAcIB8keq95a/6w3ifYAADwRKAHNYOotvMQ5YtyySDScBNBWBEqADxXVtaqqrc8wUMwdPlxXvvnbcJL2AACaIlACfLCm3SQpOZ5AKVy49rxq/bPeGh6KS3sAAE10SKAUExOjH//4x9q6dWtHHB7oFNa0W3K8Q44YI8ijQWu5Zv9a2x6AjBIAXzokUFq8eLHGjRvHw3ER1ijkDk+u9WTO1rYHsGuUCJQAuOuQ+YTp06dLku67776OODzQKcpoNhmWXAOlVjectFe9MfUGwB01SoAPZRUND8RlxVtYcZt6I6MEoI3aFCitX79eU6ZMUW5urvbt2ydJ+tOf/qQNGza0y+CAYKLZZHhKc7queuNZbwDaJuBAKT8/XxdccIESExNVUFCgyspKSVJZWZkefvjhgI753nvv6ZJLLlGvXr1kGIZef/31Zvdfu3atDMPweH311VcBfX/AFQ/EDU9uU29+NpwkowSgqYADpYceekgLFy7UH/7wB8XFNf4FN3r0aH388ccBHbO8vFzDhg3TM88849fnduzYoaKiIvs1cODAgL4/4MqqUSKjFF5SAmgPYE+9kVEC0ETAd4AdO3Zo7NixHtvT0tJ0+PDhgI45ceJETZw40e/P9ejRQ8cdd1xA3xPwxS7mTmDVWzhxW/VGw0kAbRRwRikzM1PffPONx/YNGzZowIABbRqUv4YPH67MzEyNHz9ea9asaXbfyspKlZaWur0Ab45UNhRzk1EKK6k0nATQjgIOlG6++Wb953/+pz788EMZhqHvv/9ef/nLXzRr1izdeuut7TlGnzIzM/XCCy8oPz9fy5YtU3Z2tsaPH6/33nvP52fmzZun9PR0+9WnT59OGSvCj9VwMpUapbCSGtCqNzJKALwL+A4we/ZslZSU6Nxzz1VFRYXGjh2rhIQEzZo1S7fffnt7jtGn7OxsZWdn2+9zc3O1d+9ePfroo16nBSVpzpw5ysvLs9+XlpYSLMErVr2FJ9ep0n8frVJ6UstTp1bmqabOVE1tnWIddE4BUK9Nvw1++9vfqri4WB999JE2bdqkgwcP6sEHH2yvsQVk1KhR2rlzp8+vJyQkKC0tze0FeEPDyfD0/jfF9r9//NhaLd1c2OJnXGuZyCoBcNXmO0BSUpJGjBjRHmNpFwUFBcrMzAz2MBABGou5CZTCRVHJMf3+3cY/lOpMae6yzzT25O7KTE/0+bl4l1qmypo6JSd06DABhBG/7gCuU1Ytefzxx/0ezJEjR9wKxHft2qVt27bp+OOPV9++fTVnzhzt27dPL7/8siTpySefVP/+/TVo0CBVVVXpz3/+s/Lz85Wfn+/39waaYuot/OwqLled6b6t1jS1u/hos4GSI8ZQnMNQda2pyhoKugE08usOUFBQ4PZ+69atqq2tteuEvv76azkcDuXk5AQ0mC1btujcc8+131uB2bRp07RkyRIVFRWpsLAxjV5VVaVZs2Zp3759SkxM1KBBg/Tmm29q0qRJAX1/wFVjw0naA4SLrG7JijHkFiw5DEP9uyW1+FlnrEPVtTWqqGbqDUAjvwIl16X3jz/+uFJTU/XSSy+pS5cukqR///vfuu666zRmzJiABnPOOefINE2fX1+yZInb+9mzZ2v27NkBfS+gJUdoOBl2MtMTNe+KIZq77DPVmqYchqGHrxjcbDbJkhAXo7JKkVEC4CbgO8Bjjz2mVatW2UGSJHXp0kUPPfSQJkyYoF/+8pftMkAgGCpralVVW59ZoJg7vEwe2VdjT+6u3cVH1b9bUquCJMmlRQAZJQAuAl71Vlpaqh9++MFj+4EDB1RWVtamQQHBZhVyS1JyPIFSuMlMT1TuiV1bHSRJjS0CaDoJwFXAgdJPfvITXXfddXrttdf03Xff6bvvvtNrr72mG264QVdccUV7jhHodNa0W3K8Q44YI8ijQWdI4MG4ALwI+E/lhQsXatasWZoyZYqqq6tlmqbi4uJ0ww03aMGCBe05RqDT2YXcTLtFDfvBuARKAFwEfBdISkrSc889pwULFujbb7+VaZo66aSTlJyc3J7jA4KizC7kZsVbtGDqDYA3AQdKDzzwQLNf//Wvfx3ooYGga2wNQEYpWjiZegPgRcB3geXLl7u9r66u1q5duxQbG6sTTzyRQAlhrayiWhKtAaJJ49QbGSUAjQK+CzRtPinVr4SbPn26fvKTn7RpUECwkVGKPlYxNw0nAbhq10dkp6Wl6YEHHtC9997bnocFOl0ZzSajjpOMEgAv2jVQkqTDhw+rpKSkvQ8LdCoeXxJ9EuIaAiUySgBcBPzn8tNPP+323jRNFRUV6U9/+pMuvPDCNg8MCCarRon2ANHD6sxdQUYJgIuA7wJPPPGE2/uYmBh1795d06ZN05w5c9o8MCCY7Oe8UaMUNZxklAB4EfBdYNeuXe05DiCk0HAy+tjPeqM9AAAXAdcoFRYWyjRNn18DwhnF3NHHbg9Aw0kALgIOlLKysnTw4EGP7YcOHVJWVlabBgUEG+0Bog8NJwF4E3CgZJqmDMPzYaFHjhyR0+ls06CAYCOjFH1oOAnAG7/vAnl5eZIkwzB07733Kikpyf5abW2tPvzwQ51++untNkAgGGgPEH2s9gA0nATgyu9AyerIbZqmtm/frvj4ePtr8fHxGjZsmGbNmtV+IwSCwFr1RjF39HDaxdxklAA08vsusGbNGknSddddp6eeekppaWntPiggmCpralVVW59VYOotetgNJ6lRAuAi4LvAiy++2J7jAEKGlU2SpOR4AqVoYTecZNUbABd+3QXy8vL04IMPKjk52a5V8uXxxx9v08CAYLEKuZPjHXLEeC5YQGRyklEC4IVfgVJBQYGqq6vtf/vibTUcEC5oNhmd7IaTFHMDcOHXncCqT2r6byCSWBkleihFF6s9AM96A+Aq4D5KQKSyMkqpTloDRBO74SQZJQAu/K5Rai1qlBCujlTWTy+z4i26uDac9NVQF0D08btGqTX4BYNwxtRbdLJqlOpMqbrWVHwsv8cAtKFGyZX1cFwCJEQCAqXoZPVRkuqzSvGxVCYAaGON0qJFizR48GA5nU45nU4NHjxYf/zjH9trbEBQUKMUnRJiXQMl6pQA1Av4T+Z7771XTzzxhGbOnKnc3FxJ0saNG3XXXXdp9+7deuihh9ptkEBn4vEl0ckwDMXHxqiqpo6mkwBsAd8Jnn/+ef3hD3/QNddcY2+79NJLNXToUM2cOZNACWGrrKKhmJupt6jjbAiUyCgBsAQ89VZbW6sRI0Z4bM/JyVFNTY2XTwDhgYaT0SuBFgEAmgg4UJoyZYqef/55j+0vvPCC/uM//qNNgwKCiWLu6OXaIgAApDZMvUn1xdyrVq3SqFGjJEmbNm3S3r17de2117r1XKKnEsJJYzE3gVK0sZpOVpBRAtAg4DvBZ599pjPOOEOS9O2330qSunfvru7du+uzzz6z96NlAMINgVL0IqMEoKmA7wQ86w2RqnHqjfYA0aYxUCKjBKAeHdWAJmgPEL0ap97IKAGo16Y7QUVFhT799FMdOHBAdXXuf4FdeumlbRoYEAyVNbWqqq3/b5li7uhDRglAUwHfCd5++21de+21Ki4u9viaYRiqreUvMoQfK5skEShFI+t5bwRKACwBT73dfvvtuuqqq1RUVKS6ujq3F0ESwpVVyJ0c75AjhoUI0cbZ8Ly3SqbeADQIOFA6cOCA8vLylJGR0Z7jAYKqjPqkqEZGCUBTAQdKP/3pT7V27dp2HAoQfDSbjG4JZJQANBHw3eCZZ57RVVddpfXr12vIkCGKi3NfSn3HHXe0eXBAZ2t8fAmtAaKRveqNjBKABgEHSq+88oreeecdJSYmau3atW6NJQ3DIFBCWDpSWf9A3DSm3qKSveqNjBKABgHfDX71q1/pgQce0N13362YGNoxITIcYeotqtEeAEBTAUc4VVVVmjx5MkESIkopgVJUo+EkgKYCjnKmTZumpUuXtudYgKBrrFEiUIpGZJQANBXw3aC2tla/+93v9M4772jo0KEexdyPP/54mwcHdDZr6i2VYu6oRHsAAE0FHCht375dw4cPlyR99tlnbl9zLewGwomVUUpl6i0qWe0BmHoDYAn4brBmzRqfX9u2bVughwWCioaT0c3KKBUfqVRRyTFlpicGeUQAgq3dKrFLSkr03HPPKScnRzk5Oe11WKBTlVXUtwegmDs6fbjrkCTp6x+O6Kz572rp5sIgjwhAsLU5UHr33Xc1ZcoUZWZm6ve//70mTpyoLVu2BHSs9957T5dccol69eolwzD0+uuvt/iZdevWKScnR06nUwMGDNDChQsD+t6ARDF3NCsqOaYlH+y239eZ0txln6mo5FjwBgUg6AIKlL777js99NBDGjBggK655hp16dJF1dXVys/P10MPPWTXLvmrvLxcw4YN0zPPPNOq/Xft2qVJkyZpzJgxKigo0Ny5c3XHHXcoPz8/oO8PWIESDSejz67icpmm+7Za09Tu4qPBGRCAkOD33WDSpEnasGGDLr74Yv3+97/XhRdeKIfD0S6ZnIkTJ2rixImt3n/hwoXq27evnnzySUnSqaeeqi1btujRRx/VlVde2ebxIPo0Npxk1Vu0yeqWrBijPpNkcRiG+ndLCt6gAASd3xmlVatW6cYbb9T999+viy66SA6HoyPG1SobN27UhAkT3LZdcMEF2rJli6qrq71+prKyUqWlpW4vwEIxd/TKTE/UnEmn2u8dhvTwFYMp6AainN+B0vr161VWVqYRI0bozDPP1DPPPKODBw92xNhatH//fmVkZLhty8jIUE1NjYqLi71+Zt68eUpPT7dfffr06YyhIgxU1tSqqra+fw7F3NFp6qh+9r/fuWucJo/sG8TRAAgFfgdKubm5+sMf/qCioiLdfPPN+utf/6oTTjhBdXV1Wr16tcrKyjpinD417dlkNhQZ+OrlNGfOHJWUlNivvXv3dvgYER6saTepcfUboktCbIxiY+p/dxAsA5DasOotKSlJ119/vTZs2KDt27frl7/8pebPn68ePXro0ksvbc8x+tSzZ0/t37/fbduBAwcUGxurrl27ev1MQkKC0tLS3F6AJC3d3Bg0j/3dGpaGRyHDMOxpV4JlAFI79VHKzs7W7373O3333Xd69dVX2+OQrZKbm6vVq1e7bVu1apVGjBjh8UgVoDlFJce0YNUO+z1Lw6OXlUkqq6xpYU8A0aDdGk5KksPh0OWXX64VK1YE9PkjR45o27ZtdmfvXbt2adu2bSosrP/Lfs6cObr22mvt/WfMmKE9e/YoLy9PX375pRYvXqxFixZp1qxZbT4XRBeWhsNiBUquU7EAoldITcJv2bJF5557rv0+Ly9PkjRt2jQtWbJERUVFdtAkSVlZWVq5cqXuuusuPfvss+rVq5eefvppWgPAb1ndkmUYcguWWBoendIaHoh8hIwSAIVYoHTOOefYxdjeLFmyxGPbuHHj9PHHH3fgqBANMtMTNS23n5Z8sEdSfZDE0vDoZNUokVECILXz1BsQzn6UVb8A4JSMVG24+1yWhkcpa+qtlGJuACJQAmyVNbWSpO5pCWSSopidUWLqDYAIlABbZXV9s8mEWC6LaJbK1BsAF9wRgAYV1fUZpYS44D2WB8GXmkBGCUAjAiWgQWUNGSXQRwmAO+4IQIPGQImMUjRLaWgPUMbUGwARKAE2a+rNGcdlEc0aG06y6g0AgRJgI6MESUpj1RsAFwRKQAOrPQA1StGNhpMAXHFHABpUNLQHcLLqLarZxdwESgBEoATYWPUGySWjVFWjujrfj1QCEB24IwANKu0+SlwW0Sw1oX7Vm2lKRxv+mwAQvbgjAA0o5oZUv+oxNsaQRJ0SAAIlwEZ7AEiSYRguz3ujRQAQ7bgjAA3IKMFiFXSXklECoh6BEtCAYm5YGptOEigB0Y47AtCg0p56I6MU7VJpOgmgAYES0ICMEiypDc97I6MEgDsC0MDuzE0xd9Szm06SUQKiHncEoIHdmZti7qhnrXor48G4QNQjUAIakFGCJZVibgANuCMAkmrrTFXX1j+ugvYAsFe9MfUGRD0CJUCN2SSJhpNoXPVGjRIA7giApMqG+iRJindwWUS7FFa9AWjAHQFQY2uA2BhDsQRKUc9e9UYxNxD1uCMAcn3OG/VJoOEkgEYESoBoNgl3dqDE1BsQ9bgrAHJpDUCgBNFwEkAj7gqAXJpNMvUGNTacPFJZo7o6M8ijARBMBEqAGjNK8WSUICk1oX7Vm2lKR6trW9gbQCTjrgCosT1AAhklqL6XliPGkESdEhDtCJQASRUNGSUnGSVIMgzDZeUbLQKAaMZdARAZJXhq7KVERgmIZgRKgGgPAE8ESgAkAiVAEg0n4YmmkwAkAiVAEhkleLIyShRzA9GNuwIgGk7CU2rDg3FpOglEN+4KgGg4CU8pPMYEgAiUAElklOAp1S7mpj0AEM24KwByrVEio4R6do0SU29AVCNQAtTYR8kZxyWBetbUGzVKQHTjrgCosTM3U2+wWMXc1CgB0Y27AiA6c8MTU28AJAIlQFJjMTdTb7BYDScp5gaiG3cFQC4ZJYq50YCGkwAkAiVAEu0B4CmVYm4AIlACJDW2B6DhJCwpLs96M00zyKMBECwESoAaH4pLRgmW1IT6VW+mKZVX1QZ5NACChbsCIk5RyTF98G2xikqOtfozNJxEU864GDliDEnUKQHRLDbYAwDa09LNhZqzbLvqTCnGkOZdMUSTR/Zt8XONU2/87YB6hmEoJSFWJceqdaSyWpIz2EMCEATcFRAxikqO2UGSJNWZ0txln7Uqs9Q49UZGCY0aWwSQUQKiVcgFSs8995yysrLkdDqVk5Oj9evX+9x37dq1MgzD4/XVV1914ogRKnYVl9tBkqXWNLW7+GiLn7Wn3sgowQVNJwGE1F1h6dKluvPOO3XPPfeooKBAY8aM0cSJE1VYWNjs53bs2KGioiL7NXDgwE4aMUJJVrdkNZSU2ByGof7dkpr9XE1tnWobIiwnGSW4IKMEIKQCpccff1w33HCDbrzxRp166ql68skn1adPHz3//PPNfq5Hjx7q2bOn/XI4uNlFo8z0RN08doD9PsaQHr5isDLTE5v9XEVDNkkiowR3NJ0EEDJ3haqqKm3dulUTJkxw2z5hwgR98MEHzX52+PDhyszM1Pjx47VmzZpm962srFRpaanbC5HjRwO62v9+bUZu6wq5qxuXfsc7QuaSQAhIaXgwLk0ngegVMneF4uJi1dbWKiMjw217RkaG9u/f7/UzmZmZeuGFF5Sfn69ly5YpOztb48eP13vvvefz+8ybN0/p6en2q0+fPu16Hggu17/805PiW/UZqz4pPjZGMU3n7hDVrKk3MkpA9Aq59gCG4X6jMk3TY5slOztb2dnZ9vvc3Fzt3btXjz76qMaOHev1M3PmzFFeXp79vrS0lGApgrgW3VZUt65JIM0m4UuqXczNg3GBaBUyd4Zu3brJ4XB4ZI8OHDjgkWVqzqhRo7Rz506fX09ISFBaWprbC5HD9S//Spfao+bQbBK+WDVKFHMD0StkAqX4+Hjl5ORo9erVbttXr16t0aNHt/o4BQUFyszMbO/hIUyUVTT+5V9Z7V+gRLNJNJXCg3GBqBdSU295eXmaOnWqRowYodzcXL3wwgsqLCzUjBkzJNVPm+3bt08vv/yyJOnJJ59U//79NWjQIFVVVenPf/6z8vPzlZ+fH8zTQBC53tAqaph6Q9uw6g1ASAVKkydP1qFDh/TAAw+oqKhIgwcP1sqVK9WvXz9JUlFRkVtPpaqqKs2aNUv79u1TYmKiBg0apDfffFOTJk0K1ikgyNym3vzMKDH1hqZSG1a90XASiF4hFShJ0q233qpbb73V69eWLFni9n727NmaPXt2J4wK4cL1hlbZyoyS1R6AqTc01dhwkmJuIFpxZ0BEcQuUWplRqiCjBB+YegNAoISIUloReEaJrtxoimJuANwZEFGOuK5687s9AJcD3KW6PBTXNM0W9gYQibgzIKIE0nCysT0AU29wZxVzm6Z0tKp1/z0BiCwESogogTScpD0AfHHGxcjR8Fgbmk4C0Yk7AyJGbZ2pcpe/+unMjbYyDKOxoJvHmABRiUAJEaNpr5vKVk+90R4AvvEYEyC6cWdAxGgaKFW0tuFkNRkl+Gb1UqLpJBCdCJQQMZr2uml1e4AaapTgmx0okVECohJ3BkSMpjUkra5RqmbVG3xj6g2IbgRKiBhNb2StbQ9gPTyXhpPwJqWhRQBNJ4HoxJ0BEaNpoORvRompN3jDY0yA6MadARHDY9Wbn+0BmHqDN2lO2gMA0YxACRHD+ou/S1L9VEmrp95oOIlmpCSw6g2IZtwZEDGsGpJuKQmSaDiJ9mE9GPefxeUqKjkW5NEA6GwESogYZQ0PxG0MlPxsD0AxN7z44vtSSdKH//yXzpr/rpZuLgzyiAB0Ju4MiBjW1FvXlHhJrW84WUHDSfhQVHJMr239zn5fZ0pzl31GZgmIIgRKiBhHmk69+fkIE2qU0NSu4nKZTbbVmqZ2Fx8NyngAdD7uDIgYVqDUPTWwGiVWvaGprG7JijHctzkMQ/27JQVnQAA6HYESIobVR6lrcv3UW2VNnUyzaT7AE6ve4EtmeqLmXTHEfh9jSA9fMViZ6YlBHBWAzsSdARHDKubu2jD1JrWcVTJNs3HVG8Xc8GLyyL4a0f84SdJ/XXiKJo/sG9wBAehU3BkQMRprlOLtbS0FStW1pqykE1Nv8GVwr+MkSQfKKoM7EACdjkAJEaOx4WS8XVfSUkF3hUsLAabe4Et2z1RJ0tc/lAV5JAA6G3cGRITaOlPlVfVBT6oz1l7q31JGyXrOm2FI8Q4uB3h3ckaKJGnnD0eCPBIAnY07AyJCeVXj4yVSnLFyNtQbtdR00rU1gGEYze6L6HVSj/qM0v7SCpUc45lvQDQhUEJEsFa8xTtilBDrsDNKLTWdpNkkWiM9MU4905ySpG8OMP0GRBMCJUQEqz7Jei5XQgAZJaA5Axum375m+g2IKtwdEBGOVNZPh6Q2BEpOq0aphYwSzSbRWidnUNANRCMCJUQEa+otJcE9o1TRUkbJnnrjUkDzKOgGohN3B0QEq4eSHSg1BD4tZZSsQIpmk2jJQDJKQFTi7oCIYGWU7Km3OP/aAzgp5kYLBvaozygdKKvU4aNVQR4NgM5CoISIcKTp1Fusn8XcZJTQglRnnE44rv4ZbxR0A9GDuwMiQlmllVGKk6RWtweopD0A/NC48o3pNyBaECghIrS1PYCTjBJawVr5tpNACYga3B0QEcoq6tsDNE69+dcegIwSWsOqU2LqDYgeBEqICEcq3Yu5rRqlltoDVFTTcBKtZ2eU6M4NRA3uDogITQMle9UbDSfRjk5qyCgVH6nSv8pZ+QZEAwIlRITGhpNWMbdVo9TaqTcuBbQsOSFWvbtYK9/IKgHRgLsDIoJHw0mrM3c1U29oX9kUdANRhbsDIoJVzO3xrLdWNpxMYOoNrdTYoZuCbiAaECghIng0nPSzPQAZJbSW9cy3HWSUgKjA3QFhr7bOVHlVfcDTuOqtdQ0nK8gowU+uvZRM0wzyaAB0NAIlhL3yqhr73yn2qjc/G06SUUIrndg9RYYh/ftotYqPsPINiHTcHRD2rGm3eEeMnUlKaG2NUg0ZJfgnMd6hvscnSaKgG4gGBEoIe2VNHl8iuTScbHHqjRol+G9gj/rpt3c+36+ikmNBHg2AjsTdAWHvSKX7ijfJpeFki1NvNJyE/2rq6v+7eWnjHp01/10t3VwY5BEB6CgESggbRSXH9MG3xR5/wZc1WfEmuTScbPWz3rgU0DpFJce0bsdB+32dKc1d9hmZJSBCxba8CxB8SzcXas6y7aozpRhDmnfFEE0e2VeSZ7NJqfXtAZh6g792FZer6Vq3WtPU7uKjykxPDMqYAHQc7g4IeUUlx+wgSfL8C94q5nabeovlWW/oGFndkhVjuG8zJPXvlhSU8QDoWARKCHnfHDhiB0kW6y94ycfUW1wrn/VGRgl+ykxP1LwrhshhuERLhrTv30y9AZEo5O4Ozz33nLKysuR0OpWTk6P169c3u/+6deuUk5Mjp9OpAQMGaOHChZ00UnSWtz/f77HNYRj2X/BllVZGKc7+utUeoKq2TrVNoywXFbQHQAAmj+yrDXefq1dvOlMTTsuQaUozXy3Ql0WlXuvoAISvkAqUli5dqjvvvFP33HOPCgoKNGbMGE2cOFGFhd5XlOzatUuTJk3SmDFjVFBQoLlz5+qOO+5Qfn5+QN/fW7FwuG0LlXG0dZvlH1/+oL9scv/5G5IevmKwXQ9yxEt7AKvhpCRV+cgqmaZpf42Gk/BXZnqick/spscnn64B3ZJVVFKhiU+t18//8KHbSjiub7bx8+6Ybfs76Q+SkCrmfvzxx3XDDTfoxhtvlCQ9+eSTeuedd/T8889r3rx5HvsvXLhQffv21ZNPPilJOvXUU7VlyxY9+uijuvLKK/363vlb9+rBVbvdioUleRQQh/K2nww/QcsL9gV9HG3dNnlkXxWVHNPm3f/Wr5ZvlyRNH91fPdOcmv/2V/pR1vF2IbfU2B7Adeot3tEY+FTW1Cox3jNj5DotR0YJgUpJiNVvLh2kaxd/ZG+rM+v/uz5QWqkn/u9rrm+28fPugG2qqi+/6GiGGSIPK6qqqlJSUpL+9re/6Sc/+Ym9/T//8z+1bds2rVu3zuMzY8eO1fDhw/XUU0/Z25YvX66rr75aR48eVVxcnMdnKisrVVlZab8vKSlR37591efWJVI8xZjBFmNIt//4JD3z7jd2XVKv45z6+8yz9cX3JZq6aLMy0hL0j1+eY38mb2mBVn1xQPdcdIqu+VE/e/vp969STZ2pf+SNU0a60+N7lRyr1lnz35UkFfz6fMU5yCohMB/+85BueGlLsIcBRJW6yqPa9/x0HT58WOnp6R33jcwQsW/fPlOS+f7777tt/+1vf2uefPLJXj8zcOBA87e//a3btvfff9+UZH7//fdeP3PfffeZknjx4sWLFy9eEfD69ttv2ycQ8SGkpt4kyXBdSSLJNE2PbS3t7227Zc6cOcrLy7PfHz58WP369VNhYWHHRqQhprS0VH369NHevXuVlpYW7OF0Gs6b844GnDfnHQ2sGaHjjz++Q79PyARK3bp1k8Ph0P797iucDhw4oIyMDK+f6dmzp9f9Y2Nj1bVrV6+fSUhIUEJCgsf29PT0qPoPzJKWlsZ5RxHOO7pw3tElWs87JqZjyyZCpigjPj5eOTk5Wr16tdv21atXa/To0V4/k5ub67H/qlWrNGLECK/1SQAAAP4ImUBJkvLy8vTHP/5Rixcv1pdffqm77rpLhYWFmjFjhqT6abNrr73W3n/GjBnas2eP8vLy9OWXX2rx4sVatGiRZs2aFaxTAAAAESRkpt4kafLkyTp06JAeeOABFRUVafDgwVq5cqX69esnSSoqKnLrqZSVlaWVK1fqrrvu0rPPPqtevXrp6aef9qs1QEJCgu677z6v03GRjPPmvKMB5815RwPOu2PPO2TaAwAAAISakJp6AwAACCUESgAAAD4QKAEAAPhAoAQAAOADgRIAAIAPERkoPffcc8rKypLT6VROTo7Wr1/f7P7r1q1TTk6OnE6nBgwYoIULF3rsk5+fr9NOO00JCQk67bTTtHz58o4afsD8Oe9ly5bp/PPPV/fu3ZWWlqbc3Fy98847bvssWbJEhmF4vCoqKjr6VPziz3mvXbvW6zl99dVXbvtF2s97+vTpXs970KBB9j6h/vN+7733dMkll6hXr14yDEOvv/56i5+JhGvb3/OOlGvb3/OOlGvb3/OOhGtbkubNm6eRI0cqNTVVPXr00OWXX64dO3a0+LnOuMYjLlBaunSp7rzzTt1zzz0qKCjQmDFjNHHiRLf+S6527dqlSZMmacyYMSooKNDcuXN1xx13KD8/395n48aNmjx5sqZOnapPPvlEU6dO1dVXX60PP/yws06rRf6e93vvvafzzz9fK1eu1NatW3XuuefqkksuUUFBgdt+aWlpKioqcns5nc7OOKVW8fe8LTt27HA7p4EDB9pfi8Sf91NPPeV2vnv37tXxxx+vq666ym2/UP55l5eXa9iwYXrmmWdatX+kXNv+nnekXNv+nrcl3K9tf887Eq5tqT7gue2227Rp0yatXr1aNTU1mjBhgsrLy31+ptOu8Q595G4Q/OhHPzJnzJjhtu2UU04x7777bq/7z5492zzllFPctt18883mqFGj7PdXX321eeGFF7rtc8EFF5g/+9nP2mnUbefveXtz2mmnmffff7/9/sUXXzTT09Pba4gdwt/zXrNmjSnJ/Pe//+3zmNHw816+fLlpGIa5e/due1s4/Lwtkszly5c3u0+kXNuuWnPe3oTjte2qNecdKde2q0B+3uF+bVsOHDhgSjLXrVvnc5/OusYjKqNUVVWlrVu3asKECW7bJ0yYoA8++MDrZzZu3Oix/wUXXKAtW7aourq62X18HbOzBXLeTdXV1amsrMzjKcxHjhxRv3791Lt3b1188cUef5UGU1vOe/jw4crMzNT48eO1Zs0at69Fw8970aJFOu+88+yu95ZQ/nn7KxKu7fYQjtd2W4Tztd0eIuXaLikpkSSP/25dddY1HlGBUnFxsWpra5WRkeG2PSMjQ/v37/f6mf3793vdv6amRsXFxc3u4+uYnS2Q827qscceU3l5ua6++mp72ymnnKIlS5ZoxYoVevXVV+V0OnXWWWdp586d7Tr+QAVy3pmZmXrhhReUn5+vZcuWKTs7W+PHj9d7771n7xPpP++ioiK99dZbuvHGG922h/rP21+RcG23h3C8tgMRCdd2W0XKtW2apvLy8nT22Wdr8ODBPvfrrGs8pJ711l4Mw3B7b5qmx7aW9m+63d9jBkOgY3z11Vf1m9/8Rm+88YZ69Ohhbx81apRGjRplvz/rrLN0xhln6Pe//72efvrp9ht4G/lz3tnZ2crOzrbf5+bmau/evXr00Uc1duzYgI4ZLIGOccmSJTruuON0+eWXu20Pl5+3PyLl2g5UuF/b/oikaztQkXJt33777fr000+1YcOGFvftjGs8ojJK3bp1k8Ph8IgUDxw44BFRWnr27Ol1/9jYWHXt2rXZfXwds7MFct6WpUuX6oYbbtD//M//6Lzzzmt235iYGI0cOTJk/gppy3m7GjVqlNs5RfLP2zRNLV68WFOnTlV8fHyz+4baz9tfkXBtt0U4X9vtJdyu7baIlGt75syZWrFihdasWaPevXs3u29nXeMRFSjFx8crJydHq1evdtu+evVqjR492utncnNzPfZftWqVRowYobi4uGb38XXMzhbIeUv1f21Onz5dr7zyii666KIWv49pmtq2bZsyMzPbPOb2EOh5N1VQUOB2TpH685bqV5Z88803uuGGG1r8PqH28/ZXJFzbgQr3a7u9hNu13Rbhfm2bpqnbb79dy5Yt07vvvqusrKwWP9Np13iry77DxF//+lczLi7OXLRokfnFF1+Yd955p5mcnGyvALj77rvNqVOn2vv/85//NJOSksy77rrL/OKLL8xFixaZcXFx5muvvWbv8/7775sOh8OcP3+++eWXX5rz5883Y2NjzU2bNnX6+fni73m/8sorZmxsrPnss8+aRUVF9uvw4cP2Pr/5zW/Mt99+2/z222/NgoIC87rrrjNjY2PNDz/8sNPPzxd/z/uJJ54wly9fbn799dfmZ599Zt59992mJDM/P9/eJxJ/3pYpU6aYZ555ptdjhvrPu6yszCwoKDALCgpMSebjjz9uFhQUmHv27DFNM3KvbX/PO1KubX/PO1KubX/P2xLO17ZpmuYtt9xipqenm2vXrnX77/bo0aP2PsG6xiMuUDJN03z22WfNfv36mfHx8eYZZ5zhtrxw2rRp5rhx49z2X7t2rTl8+HAzPj7e7N+/v/n88897HPNvf/ubmZ2dbcbFxZmnnHKK28UXKvw573HjxpmSPF7Tpk2z97nzzjvNvn37mvHx8Wb37t3NCRMmmB988EEnnlHr+HPejzzyiHniiSeaTqfT7NKli3n22Webb775pscxI+3nbZqmefjwYTMxMdF84YUXvB4v1H/e1vJvX//NRuq17e95R8q17e95R8q1Hch/5+F+bZum6fWcJZkvvviivU+wrnGjYYAAAABoIqJqlAAAANoTgRIAAIAPBEoAAAA+ECgBAAD4QKAEAADgA4ESAACADwRKAAAAPhAoAQAA+ECgBCBinHPOOTIMQ4ZhaNu2bW061vTp0+1jvf766+0yPgDhh0AJQES56aabVFRUpMGDB7fpOE899ZSKioraaVQAwlVssAcAAO0pKSlJPXv2bPNx0tPTlZ6e3g4jAhDOyCgBCFmvvvqqnE6n9u3bZ2+78cYbNXToUJWUlLT6OOecc45mzpypO++8U126dFFGRoZeeOEFlZeX67rrrlNqaqpOPPFEvfXWWx1xGgDCGIESgJD1s5/9TNnZ2Zo3b54k6f7779c777yjt956y+9sz0svvaRu3brpo48+0syZM3XLLbfoqquu0ujRo/Xxxx/rggsu0NSpU3X06NGOOBUAYYpACUDIMgxDv/3tb/XHP/5RDz/8sJ566im9/fbbOuGEE/w+1rBhw/SrX/1KAwcO1Jw5c5SYmKhu3brppptu0sCBA/XrX/9ahw4d0qefftoBZwIgXFGjBCCkXXzxxTrttNN0//33a9WqVRo0aFBAxxk6dKj9b4fDoa5du2rIkCH2toyMDEnSgQMH2jZgABGFjBKAkPbOO+/oq6++Um1trR3MBCIuLs7tvWEYbtsMw5Ak1dXVBfw9AEQeAiUAIevjjz/WVVddpf/+7//WBRdcoHvvvTfYQwIQZZh6AxCSdu/erYsuukh33323pk6dqtNOO00jR47U1q1blZOTE+zhAYgSZJQAhJx//etfmjhxoi699FLNnTtXkpSTk6NLLrlE99xzT5BHByCakFECEHKOP/54ffnllx7b33jjjYCOt3btWo9tu3fv9thmmmZAxwcQucgoAYgozz33nFJSUrR9+/Y2HWfGjBlKSUlpp1EBCFeGyZ9QACLEvn37dOzYMUlS3759FR8fH/CxDhw4oNLSUklSZmamkpOT22WMAMILgRIAAIAPTL0BAAD4QKAEAADgA4ESAACADwRKAAAAPhAoAQAA+ECgBAAA4AOBEgAAgA8ESgAAAD4QKAEAAPhAoAQAAODD/wdO9TbLEUfNhQAAAABJRU5ErkJggg==",
+ "image/png": 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"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
@@ -600,7 +561,7 @@
}
],
"source": [
- "plot_1D(x, p_all)"
+ "plot_1D(x, p_all, step=1500)"
]
},
{
diff --git a/content/Week_2_1/WS_2_1_wiggle.html b/src/students/Week_2_1/WS_2_1_solution.html
similarity index 85%
rename from content/Week_2_1/WS_2_1_wiggle.html
rename to src/students/Week_2_1/WS_2_1_solution.html
index 2b5dc10e..ad426ccd 100644
--- a/content/Week_2_1/WS_2_1_wiggle.html
+++ b/src/students/Week_2_1/WS_2_1_solution.html
@@ -3,7 +3,7 @@
<html lang="en">
<head><meta charset="utf-8"/>
<meta content="width=device-width, initial-scale=1.0" name="viewport"/>
-<title>WS_2_1_wiggle</title><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script><script>
+<title>WS_2_1_solution</title><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script><script>
(function() {
function addWidgetsRenderer() {
var mimeElement = document.querySelector('script[type="application/vnd.jupyter.widget-view+json"]');
@@ -7524,16 +7524,73 @@ a.anchor-link {
</div>
</div>
</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=1f814151-32e0-4a2c-809a-29f57ea40290">
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+<div style="background-color:#FAE99E; color: black; width: 95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px">
+<p>
+<b>General comments to start off the solution:</b>
+</p>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=0bbcc9be-71bc-4bb3-b665-58c64339747d">
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+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<ol>
+<li>This is in general how the code works: you should have seen that for each case, once you define the Python variables, there are ready-made functions to complete the analysis: first by running the simulation (<code>run_simulation_1D</code>) which initializes the volumes (<code>initialize_1D</code>) then sets up the time (the loop over <code>t</code>) and space integration (<code>advection_1D</code>). Then you can plot the initial condition (<code>plot_1D</code>) and visualize each time step (<code>plot_1D_all</code>).</li>
+<li>Applying the cyclic boundary condition is very simple: you only need to shift the indexing from the "math" in the textbook by 1 when implementing in Python. This does introduce a slight error since you are actually calculating $phi$ for a volume to the left of your index; however, for small volumes it is negligible (and you could shift it back in each time step, if you wanted).</li>
+<li>Note also that the cyclic boundary does not have any mathematical basis, and is not modelling "reality" in any way. It is a convenient "trick" that we use to make it easy to observe how the wave moves in space without worrying about the particular location of the wave (x) at any time.</li>
+</ol>
+<p>Key things to notice about the activities in this assignment:</p>
+<ol>
+<li>In Part 1, we see that the central scheme is <em>very</em> unstable (default settings).</li>
+<li>In Part 2: making the initial condition smooth helps...for a short time (set <code>square=False</code>).</li>
+<li>In Part 3: upwinding becomes (conditionally) stable; if CFL<1.0, you will see false diffusion.</li>
+<li>In Part 4: we use the CFL number to confirm stability regions. Note that if you use a CFL of 0.8 and your solution is unstable, you implemented the upwinding scheme incorrectly. Check the tips above about the cyclic indexing to help solve your issue; note also that regardless of if or how you implemented the cyclic boundary condition, if you are using points that are to the "right" of the index for <code>p_new</code> then you did not implement upwinding correctly (for example, if you compute <code>p_new[i]</code> and the calculation includes a point <code>p[i + 1]</code>).</li>
+</ol>
+<p>The reason we notice the above points is because our PDE is convection (hyperbolic) and our pulse is moving to the right, which implies that the upwind cells (volumes) are more important (they have a larger weight). Even though backward difference (the upwind scheme) is a lower-accuracy method (first order) than central averaging (second order), it is more stable.</p>
+<p>It is important to recognize <strong>three types of numerical issues</strong> that are present in this assignment:</p>
+<ol>
+<li>Instability caused by the nature of the PDE (a hyperbolic equation), combined with the numerical scheme (central averaging in space and forward Euler in time).</li>
+<li>Instability as described by the CFL criterion.</li>
+<li>Numerical diffusion (false diffusion), which is inherent in upwind schemes (an explanation is outside of the scope of MUDE: we are happy as long as you recognize this can be an issue!).</li>
+</ol>
+<p><em>After the general comments here, the solution has been implemented in the code below. There is also a large section of code that facilitates the use of dictionaries to keep track of analysis cases; it's not part of the MUDE exam material, but you might find it useful when working on your projects, especially if you are working on a situation when you would like to evaluate a lot of scenarios and keep track of the input parameters. For example, you can see that each dictionary stores the variable values and a name describing it.</em></p>
+</div>
+</div>
+</div>
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+<div style="background-color:#FAE99E; color: black; width: 95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px">
+<p>
+<b>End general comments.</b>
+</p>
+</div>
+</div>
+</div>
+</div>
+</div>
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-<h2 id="Overview:">Overview:<a class="anchor-link" href="#Overview:">¶</a></h2><p>In this workshop the advection problem from the textbook is treated first in 1D and then in 2D. R</p>
-$$
-\frac{\partial \phi}{\partial t} + c\frac{\partial \phi}{\partial x} = 0
-$$<p>There are two main objectives:</p>
+<h2 id="Overview:">Overview:<a class="anchor-link" href="#Overview:">¶</a></h2><p>In this workshop the [advection problem covered in the textbook] is treated first in 1D and then in 2D. There are two main objectives:</p>
<ol>
<li>Understand the advection problem itself (how the quantity of interest is transported by the velocity field)</li>
<li>Explore characteristics of the numerical analysis schemes employed, in particular: numerical diffusion and FVM stability</li>
@@ -7570,9 +7627,8 @@ Nx -> Nx, Ny
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-<h2 id="Part-1:-Implement-Central-Averaging">Part 1: Implement Central Averaging<a class="anchor-link" href="#Part-1:-Implement-Central-Averaging">¶</a></h2><p>We are going to implement the central averaging scheme as derived in the textbook; however, <strong>instead of implementing the system of equations in a matrix formulation</strong>, we will <em>loop over each of the finite volumes in the system,</em> one at a time.</p>
+<h2 id="Part-1:-Implement-Central-Difference">Part 1: Implement Central Difference<a class="anchor-link" href="#Part-1:-Implement-Central-Difference">¶</a></h2><p>We are going to implement the central difference scheme as derived in the textbook; however, <strong>instead of implementing the system of equations in a matrix formulation</strong>, we will <em>loop over each of the finite volumes in the system,</em> one at a time.</p>
<p>Because we will want to watch the "pulse" travel over a long period of time, we will take advantage of the reverse-indexing of Python (i.e., the fact that an index <code>a[-3]</code>, for example, will access the third item from the end of the array or list). When taking the volumes to the left of the first volume in direction $x$, we can use the values of $phi$ from the "last" volumes in $x$ (the end of the array). All we need to do is shift the index for $phi_i$ such that we avoid a situation where <code>i+1</code> "breaks" the loop (because the maximum index is <code>i</code>). In other words, only volumes with index <code>i</code> or smaller should be used (e.g., instead of <code>i-1</code>, <code>i</code>, and <code>i+1</code>, use <code>i-2</code>, <code>i-1</code> and <code>i</code>.</p>
-<p><em>Note: remmeber that the term "central difference" was used in the finite difference method; we use the term "central averaging" here, or "linear interpolation," as used in the book, to indicate that the finite volume method is interpolating across the volume (using the boundaries/faces).</em></p>
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@@ -7594,7 +7650,7 @@ $$</p></div>
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+<div class="jp-InputPrompt jp-InputArea-prompt">In [21]:</div>
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<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
@@ -7628,7 +7684,7 @@ $$</p></div>
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<div class="highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">initialize_1D</span><span class="p">(</span><span class="n">p0</span><span class="p">,</span> <span class="n">L</span><span class="p">,</span> <span class="n">Nx</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">Nt</span><span class="p">,</span> <span class="n">square</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
@@ -7666,7 +7722,7 @@ $$</p></div>
<span class="sd"> Arguments are defined elsewhere, except one keyword argument</span>
<span class="sd"> defines the shape of the initial condition.</span>
-
+<span class="sd"> </span>
<span class="sd"> square : bool</span>
<span class="sd"> - specifies a square pulse if True</span>
<span class="sd"> - specifies a Gaussian shape if False</span>
@@ -7677,7 +7733,9 @@ $$</p></div>
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">dx</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">L</span> <span class="o">-</span> <span class="n">dx</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">Nx</span><span class="p">)</span>
-
+ <span class="c1"># Initialise domain:</span>
+ <span class="c1"># - a square pulse with p0 between 0.5 and 1</span>
+ <span class="c1"># - a Gaussian shape around 1</span>
<span class="k">if</span> <span class="n">square</span><span class="p">:</span>
<span class="n">p_init</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">Nx</span><span class="p">)</span>
<span class="n">p_init</span><span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="mf">.5</span><span class="o">/</span><span class="n">dx</span><span class="p">):</span><span class="nb">int</span><span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="n">dx</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span> <span class="o">=</span> <span class="n">p0</span>
@@ -7693,9 +7751,11 @@ $$</p></div>
<span class="n">p_new</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">Nx</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">Nx</span><span class="p">):</span>
<span class="k">if</span> <span class="n">central</span><span class="p">:</span>
- <span class="k">pass</span> <span class="c1"># add central averaging + FE scheme here (remove pass)</span>
+ <span class="c1"># pass # add central averaging + FE scheme here (remove pass)</span>
+ <span class="n">p_new</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="mf">0.5</span><span class="o">*</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">dt</span><span class="o">/</span><span class="n">dx</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="n">p</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
- <span class="k">pass</span> <span class="c1"># add upwind + FE scheme here (remove pass)</span>
+ <span class="c1"># pass # add upwind + FE scheme here (remove pass)</span>
+ <span class="n">p_new</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="o">*</span><span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">dt</span><span class="o">/</span><span class="n">dx</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="n">p</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">return</span> <span class="n">p_new</span>
<span class="k">def</span> <span class="nf">run_simulation_1D</span><span class="p">(</span><span class="n">p0</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">L</span><span class="p">,</span> <span class="n">Nx</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">Nt</span><span class="p">,</span> <span class="n">dx</span><span class="p">,</span> <span class="n">dt</span><span class="p">,</span>
@@ -7750,7 +7810,7 @@ $$</p></div>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">' dt [ s ]: </span><span class="si">{</span><span class="n">dt</span><span class="si">:</span><span class="s1">0.2e</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'Using central difference?: </span><span class="si">{</span><span class="n">central</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'Using square init. cond.?: </span><span class="si">{</span><span class="n">square</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
- <span class="n">calculated_CFL</span> <span class="o">=</span> <span class="kc">None</span>
+ <span class="n">calculated_CFL</span> <span class="o">=</span> <span class="n">c</span><span class="o">*</span><span class="n">dt</span><span class="o">/</span><span class="n">dx</span>
<span class="k">if</span> <span class="n">calculated_CFL</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'CFL not calculated yet.'</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
@@ -7761,6 +7821,182 @@ $$</p></div>
</div>
</div>
</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=ff756348-5d90-4063-afa0-dc78ba2059e1">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<div style="background-color:#facb8e; color: black; width: 95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px">
+<p>
+<b>Start of code to define a dictionary to help keep track of analysis "cases." This is not part of the handout.</b>
+</p>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=6a3b1aa0-784b-4996-b987-4f90958c5c61">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p>To help present specific cases in the solution, a dictionary is used to store the key Python variable values that define the problem of interest are stored:</p>
+<pre><code>p0, c, L, Nx, T, Nt, dx, dt, central
+</code></pre>
+<p>Each case is stored as an elemetn of a list <code>C</code>, and a few functions are created to facilitate usage.</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=fb0c4d1e-7fce-480d-96c7-7bddcffd525c">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [23]:</div>
+<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="cm-editor cm-s-jupyter">
+<div class="highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">case_create</span><span class="p">(</span><span class="n">p0</span><span class="o">=</span><span class="mf">2.0</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="mf">5.0</span><span class="p">,</span> <span class="n">L</span><span class="o">=</span><span class="mf">2.0</span><span class="p">,</span> <span class="n">Nx</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
+ <span class="n">T</span><span class="o">=</span><span class="mf">4.0</span><span class="p">,</span> <span class="n">Nt</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span>
+ <span class="n">central</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">square</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">'''Store variables defining case in a dict.</span>
+<span class="sd"> </span>
+<span class="sd"> For use in the solution.</span>
+<span class="sd"> '''</span>
+ <span class="n">C</span> <span class="o">=</span> <span class="p">{}</span>
+ <span class="n">C</span><span class="p">[</span><span class="s1">'p0'</span><span class="p">]</span> <span class="o">=</span> <span class="n">p0</span>
+ <span class="n">C</span><span class="p">[</span><span class="s1">'c'</span><span class="p">]</span> <span class="o">=</span> <span class="n">c</span>
+ <span class="n">C</span><span class="p">[</span><span class="s1">'L'</span><span class="p">]</span> <span class="o">=</span> <span class="n">L</span>
+ <span class="n">C</span><span class="p">[</span><span class="s1">'Nx'</span><span class="p">]</span> <span class="o">=</span> <span class="n">Nx</span>
+ <span class="n">C</span><span class="p">[</span><span class="s1">'T'</span><span class="p">]</span> <span class="o">=</span> <span class="n">T</span>
+ <span class="n">C</span><span class="p">[</span><span class="s1">'Nt'</span><span class="p">]</span> <span class="o">=</span> <span class="n">Nt</span>
+
+ <span class="n">C</span><span class="p">[</span><span class="s1">'dx'</span><span class="p">]</span> <span class="o">=</span> <span class="n">L</span><span class="o">/</span><span class="n">Nx</span>
+ <span class="n">C</span><span class="p">[</span><span class="s1">'dt'</span><span class="p">]</span> <span class="o">=</span> <span class="n">T</span><span class="o">/</span><span class="n">Nt</span>
+
+ <span class="n">C</span><span class="p">[</span><span class="s1">'central'</span><span class="p">]</span> <span class="o">=</span> <span class="n">central</span>
+ <span class="n">C</span><span class="p">[</span><span class="s1">'square'</span><span class="p">]</span> <span class="o">=</span> <span class="n">square</span>
+
+ <span class="k">return</span> <span class="n">C</span>
+
+<span class="k">def</span> <span class="nf">case_set</span><span class="p">(</span><span class="n">C</span><span class="p">):</span>
+ <span class="k">return</span> <span class="p">(</span><span class="n">C</span><span class="p">[</span><span class="s1">'p0'</span><span class="p">],</span> <span class="n">C</span><span class="p">[</span><span class="s1">'c'</span><span class="p">],</span> <span class="n">C</span><span class="p">[</span><span class="s1">'L'</span><span class="p">],</span> <span class="n">C</span><span class="p">[</span><span class="s1">'Nx'</span><span class="p">],</span>
+ <span class="n">C</span><span class="p">[</span><span class="s1">'T'</span><span class="p">],</span> <span class="n">C</span><span class="p">[</span><span class="s1">'Nt'</span><span class="p">],</span> <span class="n">C</span><span class="p">[</span><span class="s1">'dx'</span><span class="p">],</span> <span class="n">C</span><span class="p">[</span><span class="s1">'dt'</span><span class="p">],</span>
+ <span class="n">C</span><span class="p">[</span><span class="s1">'central'</span><span class="p">],</span> <span class="n">C</span><span class="p">[</span><span class="s1">'square'</span><span class="p">])</span>
+</pre></div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=573e6eeb-a667-4efb-a50e-894a49dfe549">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p>Define a few cases of interest:</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=6f7306d6-c303-4cfb-bd24-2eb2976b695c">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [24]:</div>
+<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="cm-editor cm-s-jupyter">
+<div class="highlight hl-ipython3"><pre><span></span><span class="n">C</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="n">C</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">case_create</span><span class="p">())</span>
+<span class="n">C</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="s1">'name'</span><span class="p">]</span> <span class="o">=</span> <span class="s1">'Case 0: default values, central diff, square'</span>
+
+<span class="n">C</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">case_create</span><span class="p">(</span><span class="n">square</span><span class="o">=</span><span class="kc">False</span><span class="p">))</span>
+<span class="n">C</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="s1">'name'</span><span class="p">]</span> <span class="o">=</span> <span class="s1">'Case 1: default values, central diff, smooth'</span>
+
+<span class="n">C</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">case_create</span><span class="p">(</span><span class="n">central</span><span class="o">=</span><span class="kc">False</span><span class="p">))</span>
+<span class="n">C</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="s1">'name'</span><span class="p">]</span> <span class="o">=</span> <span class="s1">'Case 2: default values, backward diff, square'</span>
+
+<span class="n">C</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">case_create</span><span class="p">(</span><span class="n">central</span><span class="o">=</span><span class="kc">False</span><span class="p">))</span>
+<span class="n">C</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="s1">'name'</span><span class="p">]</span> <span class="o">=</span> <span class="s1">'Case 3: default values, backward diff, smooth'</span>
+
+<span class="n">C</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">case_create</span><span class="p">(</span><span class="n">L</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">Nx</span><span class="o">=</span><span class="mi">500</span><span class="p">,</span> <span class="n">Nt</span><span class="o">=</span><span class="mi">10000</span><span class="p">))</span>
+<span class="n">C</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="s1">'name'</span><span class="p">]</span> <span class="o">=</span> <span class="s1">'Case 4: this is unstable, more slowly, central diff'</span>
+
+<span class="n">C</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">case_create</span><span class="p">(</span><span class="n">L</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">Nx</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">T</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">Nt</span><span class="o">=</span><span class="mi">10000</span><span class="p">,</span> <span class="n">central</span><span class="o">=</span><span class="kc">False</span><span class="p">))</span>
+<span class="n">C</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="s1">'name'</span><span class="p">]</span> <span class="o">=</span> <span class="s1">'Case 5: this will show numerical diffusion, backward diff'</span>
+</pre></div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=a2efe6e4-2041-41e1-9293-c0030e161605">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<p>Choose a case and check variable values:</p>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=580c0f9d-5172-40b8-b9da-8579a9485cdf">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [25]:</div>
+<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="cm-editor cm-s-jupyter">
+<div class="highlight hl-ipython3"><pre><span></span><span class="n">p0</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">L</span><span class="p">,</span> <span class="n">Nx</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">Nt</span><span class="p">,</span> <span class="n">dx</span><span class="p">,</span> <span class="n">dt</span><span class="p">,</span> <span class="n">central</span><span class="p">,</span> <span class="n">square</span> <span class="o">=</span> <span class="n">case_set</span><span class="p">(</span><span class="n">C</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span>
+<span class="n">check_variables_1D</span><span class="p">()</span>
+</pre></div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>Current variables values:
+ p0 [---]: 2.00
+ c [m/s]: 5.00
+ L [ m ]: 2.0
+ Nx [---]: 100.0
+ T [ s ]: 4.0
+ Nt [---]: 1000.0
+ dx [ m ]: 2.00e-02
+ dt [ s ]: 4.00e-03
+Using central difference?: False
+Using square init. cond.?: True
+CFL: 1.00e+00
+</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=f20b90a5-aded-4682-a086-3ca19d0205e9">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<div style="background-color:#facb8e; color: black; width: 95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px">
+<p>
+<b>End of dictionary code.</b> Note that it is used below, for example with <code>case_set</code>
+</p>
+</div>
+</div>
+</div>
+</div>
+</div>
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=feabdadd-ad60-4eea-a34a-2e8d32cf62d6">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
@@ -7776,7 +8012,7 @@ $$</p></div>
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [26]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="n">p0</span> <span class="o">=</span> <span class="mf">2.0</span>
@@ -7785,7 +8021,7 @@ $$</p></div>
<span class="n">L</span> <span class="o">=</span> <span class="mf">2.0</span>
<span class="n">Nx</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">T</span> <span class="o">=</span> <span class="mi">40</span>
-<span class="n">Nt</span> <span class="o">=</span> <span class="mi">10000</span>
+<span class="n">Nt</span> <span class="o">=</span> <span class="mi">100000</span>
<span class="n">dx</span> <span class="o">=</span> <span class="n">L</span><span class="o">/</span><span class="n">Nx</span>
<span class="n">dt</span> <span class="o">=</span> <span class="n">T</span><span class="o">/</span><span class="n">Nt</span>
@@ -7808,12 +8044,12 @@ $$</p></div>
</div>
</div>
</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=48a174cf-79c1-4598-b438-5a139abd68af">
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=48a174cf-79c1-4598-b438-5a139abd68af">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [27]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="n">check_variables_1D</span><span class="p">()</span>
@@ -7823,6 +8059,30 @@ $$</p></div>
</div>
</div>
</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>Current variables values:
+ p0 [---]: 2.00
+ c [m/s]: 5.00
+ L [ m ]: 2.0
+ Nx [---]: 100.0
+ T [ s ]: 40.0
+ Nt [---]: 100000.0
+ dx [ m ]: 2.00e-02
+ dt [ s ]: 4.00e-04
+Using central difference?: True
+Using square init. cond.?: True
+CFL: 1.00e-01
+</pre>
+</div>
+</div>
+</div>
+</div>
</div>
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=d00aa044-e55b-4339-9e70-6455aaad4a2c">
<div class="jp-Cell-inputWrapper" tabindex="0">
@@ -7834,20 +8094,32 @@ $$</p></div>
</div>
</div>
</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=bc849eb8-4c49-4691-b7f8-35985527aca4">
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=bc849eb8-4c49-4691-b7f8-35985527aca4">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [30]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
-<div class="highlight hl-ipython3"><pre><span></span><span class="n">plot_1D</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p_all</span><span class="p">)</span>
+<div class="highlight hl-ipython3"><pre><span></span><span class="n">plot_1D</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p_all</span><span class="p">,</span> <span class="n">step</span><span class="o">=</span><span class="mi">1500</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedImage jp-OutputArea-output" tabindex="0">
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"/>
+</div>
+</div>
+</div>
+</div>
</div>
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=f46abdd9-1c87-46a7-8994-e8e35346ce7a">
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@@ -7859,12 +8131,12 @@ $$</p></div>
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-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=06742685-1f3c-43d1-8657-86a0d324b79f">
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=06742685-1f3c-43d1-8657-86a0d324b79f">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [15]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="n">plot_1D_all</span><span class="p">()</span>
@@ -7873,6 +8145,42 @@ $$</p></div>
</div>
</div>
</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>Current variables values:
+ p0 [---]: 2.00
+ c [m/s]: 5.00
+ L [ m ]: 2.0
+ Nx [---]: 100.0
+ T [ s ]: 40.0
+ Nt [---]: 100000.0
+ dx [ m ]: 2.00e-02
+ dt [ s ]: 4.00e-04
+Using central difference?: True
+Using square init. cond.?: True
+CFL: 1.00e-01
+</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>interactive(children=(Play(value=0, description='step', max=99999), Output()), _dom_classes=('widget-interact'…</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[15]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>HBox(children=(IntSlider(value=0, max=99999),))</pre>
+</div>
+</div>
+</div>
+</div>
</div>
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=62204ce3-0e2f-4641-9615-3cc1d1fe4a24">
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@@ -7881,7 +8189,7 @@ $$</p></div>
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
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<h2 id="Part-2:-Central-Difference-issues!">Part 2: Central Difference issues!<a class="anchor-link" href="#Part-2:-Central-Difference-issues!">¶</a></h2><p>The discretization is unstable (regardless of the time step used), largely due to weighting equally the influence by adjacent volumes in the fluxes. The hyperbolic nature of the equation implies that more weight should be given to the upstream/upwind $\phi$ values.</p>
-<p>You might think that the initial abrupt edges of the square wave are responsible for the instability. You can test this by replacing the square pulse with a smooth one.</p>
+<p>You might think that the initial abrupt edges of the square wave is responsible for the instability. You can test this by replacing the square pulse with a smooth one.</p>
</div>
</div>
</div>
@@ -7900,12 +8208,12 @@ Run the 1D simulation again using a smooth pulse. You can do this by changing th
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-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=8672fa59-e451-4271-8d12-470b8c42df67">
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=8672fa59-e451-4271-8d12-470b8c42df67">
<div class="jp-Cell-inputWrapper" tabindex="0">
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</div>
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-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [16]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="n">square</span><span class="o">=</span><span class="kc">False</span>
@@ -7916,6 +8224,42 @@ Run the 1D simulation again using a smooth pulse. You can do this by changing th
</div>
</div>
</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>Current variables values:
+ p0 [---]: 2.00
+ c [m/s]: 5.00
+ L [ m ]: 2.0
+ Nx [---]: 100.0
+ T [ s ]: 40.0
+ Nt [---]: 100000.0
+ dx [ m ]: 2.00e-02
+ dt [ s ]: 4.00e-04
+Using central difference?: True
+Using square init. cond.?: False
+CFL: 1.00e-01
+</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>interactive(children=(Play(value=0, description='step', max=99999), Output()), _dom_classes=('widget-interact'…</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[16]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>HBox(children=(IntSlider(value=0, max=99999),))</pre>
+</div>
+</div>
+</div>
+</div>
</div>
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=bd6bf070-db79-4e76-a44d-e9f187263975">
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@@ -7923,12 +8267,12 @@ Run the 1D simulation again using a smooth pulse. You can do this by changing th
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-<h2 id="Task-3:-Upwind-scheme">Task 3: Upwind scheme<a class="anchor-link" href="#Task-3:-Upwind-scheme">¶</a></h2><p>More weight can be given to the upwind cells by choosing $\phi$ values for the East face $\phi_i$, and for the West face, use $\phi_{i-1}$. This holds true for positive flow directions. For negative flow directions, you should choose $\phi$ values for the East face $\phi_{i-1}$, and for the West face, use $\phi_{i}$. Note that this is less accurate than the central diffence approach but it will ensure stability.</p>
+<h2 id="Part-3:-Upwind-scheme">Part 3: Upwind scheme<a class="anchor-link" href="#Part-3:-Upwind-scheme">¶</a></h2><p>More weight can be given to the upwind cells by choosing $\phi$ values for the East face $\phi_i$, and for the West face, use $\phi_{i-1}$. This holds true for positive flow directions. For negative flow directions, you should choose $\phi$ values for the East face $\phi_{i-1}$, and for the West face, use $\phi_{i}$. Note that this is less accurate than the central diffence approach but it will ensure stability.</p>
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-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=f9ede995-1b14-453f-9bf2-69d84734f458">
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=5d969cf1">
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@@ -7950,14 +8294,18 @@ Run the 1D simulation again using a smooth pulse. You can do this by changing th
<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
-<div class="highlight hl-ipython3"><pre><span></span><span class="c1"># re-define key variables and use run_simulation_1D() and plot_1D_all()</span>
+<div class="highlight hl-ipython3"><pre><span></span><span class="n">square</span><span class="o">=</span><span class="kc">True</span>
+<span class="n">central</span><span class="o">=</span><span class="kc">False</span>
+
+<span class="n">x</span><span class="p">,</span> <span class="n">p_all</span> <span class="o">=</span> <span class="n">run_simulation_1D</span><span class="p">(</span><span class="n">p0</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">L</span><span class="p">,</span> <span class="n">Nx</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="mi">10000</span><span class="p">,</span> <span class="n">dx</span><span class="p">,</span> <span class="n">dt</span><span class="p">,</span> <span class="n">central</span><span class="p">,</span> <span class="n">square</span><span class="p">)</span>
+<span class="n">plot_1D_all</span><span class="p">()</span>
</pre></div>
</div>
</div>
</div>
</div>
</div>
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=4d58d9a5">
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=37d4be76">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
@@ -7971,7 +8319,7 @@ Run the 1D simulation again using a smooth pulse. You can do this by changing th
</div>
</div>
</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=bf1691ea">
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=84aba5f3">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
@@ -7986,13 +8334,12 @@ Run the 1D simulation again using a smooth pulse. You can do this by changing th
</div>
</div>
</div>
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=92b93620">
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=3aa5d98a">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
-<p><em>Write your time stepts here, along with the result:</em></p>
<table>
<thead>
<tr>
@@ -8007,11 +8354,12 @@ Run the 1D simulation again using a smooth pulse. You can do this by changing th
</tr>
</tbody>
</table>
+<p><strong>SOLUTION NEEDED</strong></p>
</div>
</div>
</div>
</div>
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=c96ba55d-733b-4de6-9b5a-101a520031ee">
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=77365343">
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<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
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@@ -8027,7 +8375,7 @@ $$</p>
</div>
</div>
</div>
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=0704a3fd">
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=aa8b24c5">
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<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
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@@ -8042,7 +8390,7 @@ If you have not already done so, modify the function above to calculate the CFL
</div>
</div>
</div>
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=ebfceb93">
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=38784716">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
@@ -8068,8 +8416,88 @@ If you have not already done so, modify the function above to calculate the CFL
</div>
</div>
</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=faf77fd1-0c67-4452-88d4-51dcc88768dc">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=bcde4e4b">
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [52]:</div>
+<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="cm-editor cm-s-jupyter">
+<div class="highlight hl-ipython3"><pre><span></span><span class="n">choose_case</span> <span class="o">=</span> <span class="mi">5</span>
+<span class="n">p0</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">L</span><span class="p">,</span> <span class="n">Nx</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">Nt</span><span class="p">,</span> <span class="n">dx</span><span class="p">,</span> <span class="n">dt</span><span class="p">,</span> <span class="n">central</span><span class="p">,</span> <span class="n">square</span> <span class="o">=</span> <span class="n">case_set</span><span class="p">(</span><span class="n">C</span><span class="p">[</span><span class="n">choose_case</span><span class="p">])</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">C</span><span class="p">[</span><span class="n">choose_case</span><span class="p">][</span><span class="s1">'name'</span><span class="p">])</span>
+</pre></div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>Case 5: this will show numerical diffusion, backward diff
+</pre>
+</div>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=444571d6-58af-498e-846f-72867a972625">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea">
+<div class="jp-InputPrompt jp-InputArea-prompt">In [53]:</div>
+<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
+<div class="cm-editor cm-s-jupyter">
+<div class="highlight hl-ipython3"><pre><span></span><span class="n">x</span><span class="p">,</span> <span class="n">p_all</span> <span class="o">=</span> <span class="n">run_simulation_1D</span><span class="p">(</span><span class="n">p0</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">L</span><span class="p">,</span> <span class="n">Nx</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">Nt</span><span class="p">,</span> <span class="n">dx</span><span class="p">,</span> <span class="n">dt</span><span class="p">,</span> <span class="n">central</span><span class="p">,</span> <span class="n">square</span><span class="p">)</span>
+<span class="n">plot_1D_all</span><span class="p">()</span>
+</pre></div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>Current variables values:
+ p0 [---]: 2.00
+ c [m/s]: 5.00
+ L [ m ]: 10.0
+ Nx [---]: 100.0
+ T [ s ]: 4.0
+ Nt [---]: 10000.0
+ dx [ m ]: 1.00e-01
+ dt [ s ]: 4.00e-04
+Using central difference?: False
+Using square init. cond.?: True
+CFL: 2.00e-02
+</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>interactive(children=(Play(value=0, description='step', max=9999), Output()), _dom_classes=('widget-interact',…</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[53]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>HBox(children=(IntSlider(value=0, max=9999),))</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=bfd17cd8">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
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@@ -8083,22 +8511,22 @@ If you have not already done so, modify the function above to calculate the CFL
</div>
</div>
</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=faf77fd1-0c67-4452-88d4-51dcc88768dc">
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=1f919d93">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [59]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
-<div class="highlight hl-ipython3"><pre><span></span><span class="c1"># re-define key variables and use run_simulation_1D() and plot_1D_all()</span>
+<div class="highlight hl-ipython3"><pre><span></span><span class="c1"># SOLUTION</span>
</pre></div>
</div>
</div>
</div>
</div>
</div>
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=f1549927">
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=99e5acac">
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@@ -8112,7 +8540,7 @@ If you have not already done so, modify the function above to calculate the CFL
</div>
</div>
</div>
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=9f952992">
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=788b5742">
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<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
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@@ -8127,22 +8555,22 @@ If you have not already done so, modify the function above to calculate the CFL
</div>
</div>
</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=8d2ad587">
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=4cb62a90">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [60]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
-<div class="highlight hl-ipython3"><pre><span></span><span class="c1"># re-define key variables and use run_simulation_1D() and plot_1D_all()</span>
+<div class="highlight hl-ipython3"><pre><span></span><span class="c1"># SOLUTION</span>
</pre></div>
</div>
</div>
</div>
</div>
</div>
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=1858199e">
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=5c464589">
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@@ -8157,13 +8585,25 @@ If you have not already done so, modify the function above to calculate the CFL
</div>
</div>
</div>
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=26ef0f7a">
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=d9a710a7">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
-<p><em>Write your answer here.</em></p>
+<div style="background-color:#FAE99E; color: black; width: 95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px">
+<p>
+<b>Solution:</b>
+<p>The phenomenon you saw in the previous task is <em>numerical</em>, or <em>false</em> diffusion.
+...</p>
+<p>No!</p>
+<ul>
+<li>we observe the wave diffuses</li>
+<li>our PDE only considers convection</li>
+<li>where does this come from?!</li>
+</ul>
+</p>
+</div>
</div>
</div>
</div>
@@ -8230,7 +8670,7 @@ The code is set up in a very similar way to the 1D case above. Use it to explore
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [54]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="n">p0</span> <span class="o">=</span> <span class="mf">2.0</span>
@@ -8254,12 +8694,12 @@ The code is set up in a very similar way to the 1D case above. Use it to explore
</div>
</div>
</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=be2b163b-811d-498d-82e9-a6b56327efcd">
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=be2b163b-811d-498d-82e9-a6b56327efcd">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [55]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">initialize_2D</span><span class="p">(</span><span class="n">p0</span><span class="p">,</span> <span class="n">Lx</span><span class="p">,</span> <span class="n">Nx</span><span class="p">,</span> <span class="n">Ly</span><span class="p">,</span> <span class="n">Ny</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">Nt</span><span class="p">):</span>
@@ -8356,12 +8796,43 @@ The code is set up in a very similar way to the 1D case above. Use it to explore
</div>
</div>
</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=cbf8c749-4c91-4ec2-8849-99e9e7652f2e">
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="application/vnd.jupyter.stderr" tabindex="0">
+<pre><>:47: SyntaxWarning: invalid escape sequence '\p'
+<>:47: SyntaxWarning: invalid escape sequence '\p'
+C:\Users\rlanzafame\AppData\Local\Temp\ipykernel_26208\2412768473.py:47: SyntaxWarning: invalid escape sequence '\p'
+ ax.set_zlabel('$\phi$ [-]')
+</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=f25b48c4-f847-435c-8c78-4ff3a9fc4d15">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<div style="background-color:#FAE99E; color: black; width: 95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px">
+<p>
+Here you can check the Python variable assignments and visualize the initial conditions in the plot. Notice that we already redefine the time parameters to give a CFL of less than 1, in both directions.
+</p>
+</div>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=cbf8c749-4c91-4ec2-8849-99e9e7652f2e">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [56]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="n">T</span> <span class="o">=</span> <span class="mi">1</span>
@@ -8375,12 +8846,63 @@ The code is set up in a very similar way to the 1D case above. Use it to explore
</div>
</div>
</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=94e5c840-0373-451f-af12-2ac58138cc5e">
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>Current variables values:
+ p0 [---]: 2.00
+ cx [m/s]: 5.00
+ cy [m/s]: 5.00
+ Lx [ m ]: 2.0
+ Nx [---]: 100.0
+ Ly [ m ]: 2.0
+ Ny [---]: 100.0
+ T [ s ]: 1.0
+ Nt [---]: 1000.0
+ dx [ m ]: 2.00e-02
+ dy [ m ]: 2.00e-02
+ dt [ s ]: 1.00e-03
+Using central difference?: True
+Solution shape p_all[t_i]: (100, 100)
+Total time steps in p_all: 1001
+CFL, direction x: 2.50e-01
+CFL, direction y: 2.50e-01
+</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedImage jp-OutputArea-output" tabindex="0">
+<img alt="No description has been provided for this image" class="" 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"/>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=a2198cbe-422a-44b4-9bff-d3479befaa43">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<div style="background-color:#FAE99E; color: black; width: 95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px">
+<p>
+By default the central difference scheme is used, so you should see the numerical instability just as we did before in the 1D case.
+</p>
+</div>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=94e5c840-0373-451f-af12-2ac58138cc5e">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [57]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">p_all</span> <span class="o">=</span> <span class="n">run_simulation_2D</span><span class="p">(</span><span class="n">p0</span><span class="p">,</span> <span class="n">cx</span><span class="p">,</span> <span class="n">cy</span><span class="p">,</span> <span class="n">Lx</span><span class="p">,</span> <span class="n">Nx</span><span class="p">,</span> <span class="n">Ly</span><span class="p">,</span> <span class="n">Ny</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">Nt</span><span class="p">,</span> <span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">,</span> <span class="n">dt</span><span class="p">,</span> <span class="n">central</span><span class="p">)</span>
@@ -8390,12 +8912,69 @@ The code is set up in a very similar way to the 1D case above. Use it to explore
</div>
</div>
</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=96aec400-4cc3-412d-863d-9be6c2462f54">
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>Current variables values:
+ p0 [---]: 2.00
+ cx [m/s]: 5.00
+ cy [m/s]: 5.00
+ Lx [ m ]: 2.0
+ Nx [---]: 100.0
+ Ly [ m ]: 2.0
+ Ny [---]: 100.0
+ T [ s ]: 1.0
+ Nt [---]: 1000.0
+ dx [ m ]: 2.00e-02
+ dy [ m ]: 2.00e-02
+ dt [ s ]: 1.00e-03
+Using central difference?: True
+Solution shape p_all[t_i]: (100, 100)
+Total time steps in p_all: 1001
+CFL, direction x: 2.50e-01
+CFL, direction y: 2.50e-01
+</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>interactive(children=(Play(value=0, description='step', max=999), Output()), _dom_classes=('widget-interact',)…</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[57]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>HBox(children=(IntSlider(value=0, max=999),))</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=f29a9aef-f355-45bb-9156-7fcd5d1d547c">
+<div class="jp-Cell-inputWrapper" tabindex="0">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
+<div style="background-color:#FAE99E; color: black; width: 95%; vertical-align: middle; padding:15px; margin: 10px; border-radius: 10px">
+<p>
+Switching to the upwind scheme gives a stable solution. Note the numerical diffusion (change from cubic to bell shape). Also, as the edges of the bell shape spread outside of the X-Y domain, you will see them appear on the corners: this is a result of the fact that the iteration loops over X and Y in the meshgrid format don't properly find the "neighbor" volumes. To understand this, refer to the textbook where the matrix form of the 2D solution is presented and see how the index of the neighbor volumes is not sequential as in the for loops.
+</p>
+</div>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=96aec400-4cc3-412d-863d-9be6c2462f54">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In [58]:</div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="cm-editor cm-s-jupyter">
<div class="highlight hl-ipython3"><pre><span></span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">p_all</span> <span class="o">=</span> <span class="n">run_simulation_2D</span><span class="p">(</span><span class="n">p0</span><span class="p">,</span> <span class="n">cx</span><span class="p">,</span> <span class="n">cy</span><span class="p">,</span> <span class="n">Lx</span><span class="p">,</span> <span class="n">Nx</span><span class="p">,</span> <span class="n">Ly</span><span class="p">,</span> <span class="n">Ny</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">Nt</span><span class="p">,</span> <span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">,</span> <span class="n">dt</span><span class="p">,</span> <span class="n">central</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
@@ -8405,8 +8984,50 @@ The code is set up in a very similar way to the 1D case above. Use it to explore
</div>
</div>
</div>
+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>Current variables values:
+ p0 [---]: 2.00
+ cx [m/s]: 5.00
+ cy [m/s]: 5.00
+ Lx [ m ]: 2.0
+ Nx [---]: 100.0
+ Ly [ m ]: 2.0
+ Ny [---]: 100.0
+ T [ s ]: 1.0
+ Nt [---]: 1000.0
+ dx [ m ]: 2.00e-02
+ dy [ m ]: 2.00e-02
+ dt [ s ]: 1.00e-03
+Using central difference?: True
+Solution shape p_all[t_i]: (100, 100)
+Total time steps in p_all: 1001
+CFL, direction x: 2.50e-01
+CFL, direction y: 2.50e-01
+</pre>
+</div>
</div>
-<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=57fe2849">
+<div class="jp-OutputArea-child">
+<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
+<pre>interactive(children=(Play(value=0, description='step', max=999), Output()), _dom_classes=('widget-interact',)…</pre>
+</div>
+</div>
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+<div class="jp-OutputPrompt jp-OutputArea-prompt">Out[58]:</div>
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain" tabindex="0">
+<pre>HBox(children=(IntSlider(value=0, max=999),))</pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=f6d196c8">
<div class="jp-Cell-inputWrapper" tabindex="0">
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
@@ -8421,11 +9042,11 @@ The code is set up in a very similar way to the 1D case above. Use it to explore
article { position: relative }
</style>
<a href="http://creativecommons.org/licenses/by/4.0/" rel="license">
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