diff --git a/content/Week_2_1/WS_2_1_solution.ipynb b/content/Week_2_1/WS_2_1_solution.ipynb index 3549bcf25bbd62aff9b715e95f35caaf9acc4713..ea3e54329b772ae87c94fef759fc7fcaa5982b81 100644 --- a/content/Week_2_1/WS_2_1_solution.ipynb +++ b/content/Week_2_1/WS_2_1_solution.ipynb @@ -209,7 +209,7 @@ "Write by hand for FMV the <code>advection_1D</code> equation, compute the convective fluxes of $\\phi$ at the surfaces using a linear interpolation (central averaging). Then apply Forward Euler in time to the resulting ODE. Make sure you use the right indexing (maximum index should be <code>i</code>).\n", "\n", "$$\n", - "\\frac{\\partial \\phi}{\\partial t} = c\\frac{\\partial \\phi}{\\partial x} \n", + "\\frac{\\partial \\phi}{\\partial t} + c\\frac{\\partial \\phi}{\\partial x} = 0\n", "$$\n", " \n", "</div>" @@ -965,7 +965,7 @@ "Apply FVM by hand to the 2D advection equation. The volumes are rectangular. This is a good example of an exam problem.\n", "\n", "$$\n", - "\\frac{\\partial \\phi}{\\partial t} = c_x\\frac{\\partial \\phi}{\\partial x} + c_y\\frac{\\partial \\phi}{\\partial y} \n", + "\\frac{\\partial \\phi}{\\partial t} + c_x\\frac{\\partial \\phi}{\\partial x} + c_y\\frac{\\partial \\phi}{\\partial y} = 0\n", "$$\n", "\n", "</div>" diff --git a/content/Week_2_1/WS_2_1_wiggle.ipynb b/content/Week_2_1/WS_2_1_wiggle.ipynb index 98a91cdb997db0457ed337a59e250e73626c9291..b1dd8d88f908607413c22a6ca95503389a1a7b03 100644 --- a/content/Week_2_1/WS_2_1_wiggle.ipynb +++ b/content/Week_2_1/WS_2_1_wiggle.ipynb @@ -120,7 +120,7 @@ "Write by hand for FMV the <code>advection_1D</code> equation, compute the convective fluxes of $\\phi$ at the surfaces using a linear interpolation (central averaging). Then apply Forward Euler in time to the resulting ODE. Make sure you use the right indexing (maximum index should be <code>i</code>).\n", "\n", "$$\n", - "\\frac{\\partial \\phi}{\\partial t} = c\\frac{\\partial \\phi}{\\partial x} \n", + "\\frac{\\partial \\phi}{\\partial t} + c\\frac{\\partial \\phi}{\\partial x} = 0\n", "$$\n", " \n", "</div>" @@ -615,7 +615,7 @@ "Apply FVM by hand to the 2D advection equation. The volumes are rectangular. This is a good example of an exam problem.\n", "\n", "$$\n", - "\\frac{\\partial \\phi}{\\partial t} = c_x\\frac{\\partial \\phi}{\\partial x} + c_y\\frac{\\partial \\phi}{\\partial y} \n", + "\\frac{\\partial \\phi}{\\partial t} + c_x\\frac{\\partial \\phi}{\\partial x} + c_y\\frac{\\partial \\phi}{\\partial y} = 0\n", "$$\n", "\n", "</div>" diff --git a/src/teachers/Week_2_1/WS_2_1_solution.html b/src/teachers/Week_2_1/WS_2_1_solution.html index b695fda86743776f19153fb60a50b31856dc52ec..4b7fa9d2689609b49279141f90d4596312b64608 100644 --- a/src/teachers/Week_2_1/WS_2_1_solution.html +++ b/src/teachers/Week_2_1/WS_2_1_solution.html @@ -7714,7 +7714,7 @@ Nx -> Nx, Ny <b>Task 1.2:</b> <p>Write by hand for FMV the <code>advection_1D</code> equation, compute the convective fluxes of $\phi$ at the surfaces using a linear interpolation (central averaging). Then apply Forward Euler in time to the resulting ODE. Make sure you use the right indexing (maximum index should be <code>i</code>).</p> $$ -\frac{\partial \phi}{\partial t} = c\frac{\partial \phi}{\partial x} +\frac{\partial \phi}{\partial t} + c\frac{\partial \phi}{\partial x} = 0 $$</p></div> </div> </div> @@ -8503,7 +8503,7 @@ CFL: 2.00e-02 <b>Task 5:</b> Apply FVM by hand to the 2D advection equation. The volumes are rectangular. This is a good example of an exam problem. $$ -\frac{\partial \phi}{\partial t} = c_x\frac{\partial \phi}{\partial x} + c_y\frac{\partial \phi}{\partial y} +\frac{\partial \phi}{\partial t} + c_x\frac{\partial \phi}{\partial x} + c_y\frac{\partial \phi}{\partial y} = 0 $$</p></div> </div> </div> diff --git a/src/teachers/Week_2_1/WS_2_1_wiggle.html b/src/teachers/Week_2_1/WS_2_1_wiggle.html index 02675a4a7cbd814257f97c1e1a66384682875463..ab55db98408e92662f4ca9f4da336b529d60d0e3 100644 --- a/src/teachers/Week_2_1/WS_2_1_wiggle.html +++ b/src/teachers/Week_2_1/WS_2_1_wiggle.html @@ -7618,7 +7618,7 @@ Nx -> Nx, Ny <b>Task 1.2:</b> <p>Write by hand for FMV the <code>advection_1D</code> equation, compute the convective fluxes of $\phi$ at the surfaces using a linear interpolation (central averaging). Then apply Forward Euler in time to the resulting ODE. Make sure you use the right indexing (maximum index should be <code>i</code>).</p> $$ -\frac{\partial \phi}{\partial t} = c\frac{\partial \phi}{\partial x} +\frac{\partial \phi}{\partial t} + c\frac{\partial \phi}{\partial x} = 0 $$</p></div> </div> </div> @@ -8138,7 +8138,7 @@ Change the Python variables that define the problem and check to see if the CFL <b>Task 5:</b> Apply FVM by hand to the 2D advection equation. The volumes are rectangular. This is a good example of an exam problem. $$ -\frac{\partial \phi}{\partial t} = c_x\frac{\partial \phi}{\partial x} + c_y\frac{\partial \phi}{\partial y} +\frac{\partial \phi}{\partial t} + c_x\frac{\partial \phi}{\partial x} + c_y\frac{\partial \phi}{\partial y} = 0 $$</p></div> </div> </div>