FTCS prototyping
This commit is contained in:
philippun
parent
72509832d4
commit
be68985600
249
proto/FTCS.ipynb
249
proto/FTCS.ipynb
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"# imports\n",
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"import numpy as np"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"metadata": {},
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"outputs": [],
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"source": [
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"# environment\n",
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"dim = 2\n",
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"grid_size = {'x': 20, 'y': 20} # to start out\n",
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"domain_size = {'x': 20, 'y': 20} # to start out\n",
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"\n",
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"delta_x = domain_size['x'] / grid_size['x']\n",
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"delta_y = domain_size['y'] / grid_size['y'] \n",
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"\n",
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"alpha_x = np.ones((grid_size['x'],grid_size['y']))\n",
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"alpha_y = np.ones((grid_size['x'],grid_size['y']))\n",
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"\n",
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"max_stable_time_step_x = delta_x**2 / (2 * np.max(alpha_x))\n",
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"max_stable_time_step_y = delta_y**2 / (2 * np.max(alpha_y))\n",
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"max_stable_time_step = max_stable_time_step_x if max_stable_time_step_x <= max_stable_time_step_y else max_stable_time_step_y\n",
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"\n",
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"C_t = np.zeros((grid_size['x'],grid_size['y']))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"metadata": {},
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"outputs": [],
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"source": [
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"# initialization\n",
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"C_t[1,1] = 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"def alpha_interblock(alpha1, alpha2, harmonic=False):\n",
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" if not harmonic:\n",
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" return 0.5 * (alpha1 + alpha2)\n",
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" else:\n",
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" return 2 / ((1/alpha1) + (1/alpha2))\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"metadata": {},
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"outputs": [],
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"source": [
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"# simulating one time step\n",
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"def simulate(C_t): \n",
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" C_t1 = np.zeros((grid_size['x'],grid_size['y']))\n",
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"\n",
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" # inner cells\n",
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" for i in range(1, grid_size['x']-1):\n",
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" for j in range(1, grid_size['y']-1):\n",
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" C_t1[i,j] = C_t[i,j] \\\n",
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" + max_stable_time_step/delta_x**2 * (alpha_interblock(alpha_x[i+1,j], alpha_x[i,j]) * C_t[i+1,j]\n",
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" - (alpha_interblock(alpha_x[i+1,j], alpha_x[i,j]) + alpha_interblock(alpha_x[i-1,j], alpha_x[i,j])) * C_t[i,j] \n",
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" + alpha_interblock(alpha_x[i-1,j], alpha_x[i,j]) * C_t[i-1,j]) \\\n",
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" + max_stable_time_step/delta_y**2 * (alpha_interblock(alpha_y[i,j+1], alpha_y[i,j]) * C_t[i,j+1]\n",
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" - (alpha_interblock(alpha_y[i,j+1], alpha_y[i,j]) + alpha_interblock(alpha_y[i,j-1], alpha_y[i,j])) * C_t[i,j] \n",
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" + alpha_interblock(alpha_y[i,j-1], alpha_y[i,j]) * C_t[i,j-1])\n",
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"\n",
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" return C_t1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
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" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
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" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
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" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
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" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
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" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
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" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
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" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
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" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]]\n"
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]
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}
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],
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"source": [
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"for i in range(10):\n",
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" C_t = simulate(C_t)\n",
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"print(C_t)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0.5\n"
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]
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}
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],
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"source": [
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"print(max_stable_time_step)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.1"
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},
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"orig_nbformat": 4
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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