diff --git a/content/GA_2_1/Analysis_solution.ipynb b/content/GA_2_1/Analysis_solution.ipynb index cc8d8d0452912b1a823c44e5154d3cc6e1ace903..02c8489d2e071886ef7e6cff61b2555390d862a7 100644 --- a/content/GA_2_1/Analysis_solution.ipynb +++ b/content/GA_2_1/Analysis_solution.ipynb @@ -344,7 +344,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 12, "id": "d2caef59", "metadata": {}, "outputs": [], @@ -373,7 +373,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 13, "id": "e10227a9", "metadata": {}, "outputs": [ @@ -552,7 +552,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 14, "id": "6ae17c54", "metadata": {}, "outputs": [ @@ -610,7 +610,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 15, "id": "b4ea7975", "metadata": {}, "outputs": [ @@ -620,8 +620,8 @@ "text": [ "Solving complete!\n", " t_final = 20, Nt = 100, D = 50\n", - "Amplification factor = 2.3094180132979094\n", - "max Temp 45.16942991367422\n", + "Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) =0.400\n", + "max Temp:4.517e+01 C\n", "NOTE: min value color scale adjusted below min initial value\n" ] }, @@ -742,7 +742,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 16, "id": "611fa2fc", "metadata": {}, "outputs": [ @@ -762,7 +762,7 @@ " triangles: 36\n", " sides: 65\n", " side length: 5.0\n", - "Time taken for refinement: 0.470058 seconds\n" + "Time taken for refinement: 0.437018 seconds\n" ] }, { @@ -806,7 +806,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 17, "id": "aecff8fc", "metadata": {}, "outputs": [ @@ -816,8 +816,8 @@ "text": [ "Solving complete!\n", " t_final = 20, Nt = 100, D = 50\n", - "Amplification factor = 4.618937644341802\n", - "max Temp 3.1382130768183806e+87\n", + "Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) =1.600\n", + "max Temp:3.138e+87 C\n", "NOTE: min value color scale adjusted below min initial value\n" ] }, @@ -896,7 +896,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 18, "id": "a3c2b83a", "metadata": {}, "outputs": [ @@ -904,75 +904,86 @@ "name": "stdout", "output_type": "stream", "text": [ - "Solving complete!\n", - " t_final = 20, Nt = 100, D = 50\n", - "Amplification factor = 4.618937644341802\n", - "max Temp 3.1382130768183806e+87\n", - "==================================\n", "Solving complete!\n", " t_final = 20, Nt = 200, D = 50\n", - "Amplification factor = 2.309468822170901\n", - "max Temp 9.410406660981692e+101\n", + "Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) =0.800\n", + "max Temp:9.410e+101 C\n", "==================================\n", "Solving complete!\n", - " t_final = 20, Nt = 300, D = 50\n", - "Amplification factor = 1.5396458814472673\n", - "max Temp 1.0781139483112799e+78\n", + " t_final = 20, Nt = 250, D = 50\n", + "Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) =0.640\n", + "max Temp:2.534e+94 C\n", "==================================\n", "Solving complete!\n", - " t_final = 20, Nt = 400, D = 50\n", - "Amplification factor = 1.1547344110854505\n", - "max Temp 5.555175539228756e+18\n", + " t_final = 20, Nt = 300, D = 50\n", + "Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) =0.533\n", + "max Temp:1.078e+78 C\n", "==================================\n", "Solving complete!\n", - " t_final = 20, Nt = 500, D = 50\n", - "Amplification factor = 0.9237875288683604\n", - "max Temp 47.07455822697124\n", - "stable\n", + " t_final = 20, Nt = 350, D = 50\n", + "Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) =0.457\n", + "max Temp:8.446e+52 C\n", "==================================\n", "Solving complete!\n", - " t_final = 20, Nt = 600, D = 50\n", - "Amplification factor = 0.7698229407236337\n", - "max Temp 47.07403402998238\n", - "stable\n", + " t_final = 20, Nt = 400, D = 50\n", + "Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) =0.400\n", + "max Temp:5.555e+18 C\n", "==================================\n", "Solving complete!\n", - " t_final = 20, Nt = 700, D = 50\n", - "Amplification factor = 0.6598482349059717\n", - "max Temp 47.073658913307604\n", - "stable\n", + " t_final = 20, Nt = 450, D = 50\n", + "Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) =0.356\n", + "max Temp:4.707e+01 C\n", "==================================\n", "Solving complete!\n", - " t_final = 20, Nt = 800, D = 50\n", - "Amplification factor = 0.5773672055427252\n", - "max Temp 47.07337719857965\n", - "stable\n", + " t_final = 20, Nt = 500, D = 50\n", + "Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) =0.320\n", + "max Temp:4.707e+01 C\n", "==================================\n", "Solving complete!\n", - " t_final = 20, Nt = 900, D = 50\n", - "Amplification factor = 0.5132152938157557\n", - "max Temp 47.07315786370043\n", - "stable\n", + " t_final = 20, Nt = 550, D = 50\n", + "Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) =0.291\n", + "max Temp:4.707e+01 C\n", "==================================\n", "Solving complete!\n", - " t_final = 20, Nt = 1000, D = 50\n", - "Amplification factor = 0.4618937644341802\n", - "max Temp 47.07298225509566\n", - "stable\n", - "==================================\n", - "\n" + " t_final = 20, Nt = 600, D = 50\n", + "Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) =0.267\n", + "max Temp:4.707e+01 C\n", + "==================================\n" ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 1000x500 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ "side_length= 5.0\n", "t_final=20\n", "D=50\n", - "Nt_vec=100 * np.arange(1, 11)\n", + "Nt_vec=np.arange(200, 650, 50, dtype=int)\n", + "Stability = []\n", + "max_temp = []\n", "for Nt in Nt_vec:\n", - " mesh.solve(20, Nt=Nt, D=D)\n", + " _,stability,temp=mesh.solve(20, Nt=Nt, D=D)\n", + " Stability.append(stability)\n", + " max_temp.append(temp.max())\n", " print(\"==================================\")\n", - "print()" + "plt.figure(figsize=(10, 5))\n", + "plt.plot(Nt_vec, Stability, 'o-')\n", + "for x, y, temp in zip(Nt_vec, Stability, max_temp):\n", + " plt.text(x, y,f'$T=${temp:.1e} C', fontsize=6, ha='center', va='top')\n", + "plt.xlabel('Number of time steps')\n", + "plt.ylabel(r'D*$\\Delta t$ Surface/Volume/centroid_distance)')\n", + "plt.title('Stability criteria vs Number of time steps ')\n", + "plt.axhline(0.5, color='r', linestyle='--')\n", + "plt.grid()\n", + "plt.show()" ] }, { @@ -1004,7 +1015,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 19, "id": "7f4b3216", "metadata": {}, "outputs": [ @@ -1061,7 +1072,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 20, "id": "8f49fec6", "metadata": {}, "outputs": [ @@ -1142,7 +1153,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 21, "id": "75e81ac6", "metadata": {}, "outputs": [ @@ -1224,7 +1235,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 22, "id": "1363e10c", "metadata": {}, "outputs": [ @@ -1317,7 +1328,7 @@ ], "metadata": { "kernelspec": { - "display_name": "mude-base", + "display_name": "MUDE", "language": "python", "name": "python3" }, @@ -1331,7 +1342,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.4" + "version": "3.11.5" }, "widgets": { "application/vnd.jupyter.widget-state+json": { diff --git a/content/GA_2_1/utilities_solution.py b/content/GA_2_1/utilities_solution.py index 65404320c082c6a545f82e784f24efb1978dd04b..210fffb4e62b9c3b96cb3c55b3743521814139b0 100644 --- a/content/GA_2_1/utilities_solution.py +++ b/content/GA_2_1/utilities_solution.py @@ -20,7 +20,7 @@ class Mesh: self.get_boundary_sides() self.set_initial_conditions() - def solve(self, t_final, Nt, D): + def solve(self, t_final, Nt, D,print_results=False): unknowns = np.zeros((Nt+1, len(self.triangles))) unknowns[0, :] = self.initial_conditions @@ -67,14 +67,14 @@ class Mesh: self.Nt = Nt self.t_final = t_final print('Solving complete!') + print(f' t_final = {t_final}, Nt = {Nt}, D = {D}') - value = constant - print(r'Amplification factor =', constant) - print("max Temp",max(unknowns[-1, :])) - if constant<1: - print("stable") - - return unknowns + stability_criteria = constant/centroid_distance + print(f'Stability Criteria (D*Delta_t*Surface/Volume/centroid_distance) ={stability_criteria:.3f}') + max_temp=max(unknowns[-1, :]) + print(f"max Temp:{max_temp:.3e} C") + + return unknowns,stability_criteria,max_temp