mirror of
https://git.gfz-potsdam.de/naaice/tug.git
synced 2025-12-13 09:28:23 +01:00
FTCS prototyping
This commit is contained in:
philippun
parent
72509832d4
commit
be68985600
249
proto/FTCS.ipynb
249
proto/FTCS.ipynb
@ -0,0 +1,249 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# imports\n",
|
||||
"import numpy as np"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 25,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# environment\n",
|
||||
"dim = 2\n",
|
||||
"grid_size = {'x': 20, 'y': 20} # to start out\n",
|
||||
"domain_size = {'x': 20, 'y': 20} # to start out\n",
|
||||
"\n",
|
||||
"delta_x = domain_size['x'] / grid_size['x']\n",
|
||||
"delta_y = domain_size['y'] / grid_size['y'] \n",
|
||||
"\n",
|
||||
"alpha_x = np.ones((grid_size['x'],grid_size['y']))\n",
|
||||
"alpha_y = np.ones((grid_size['x'],grid_size['y']))\n",
|
||||
"\n",
|
||||
"max_stable_time_step_x = delta_x**2 / (2 * np.max(alpha_x))\n",
|
||||
"max_stable_time_step_y = delta_y**2 / (2 * np.max(alpha_y))\n",
|
||||
"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",
|
||||
"\n",
|
||||
"C_t = np.zeros((grid_size['x'],grid_size['y']))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 26,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# initialization\n",
|
||||
"C_t[1,1] = 1"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def alpha_interblock(alpha1, alpha2, harmonic=False):\n",
|
||||
" if not harmonic:\n",
|
||||
" return 0.5 * (alpha1 + alpha2)\n",
|
||||
" else:\n",
|
||||
" return 2 / ((1/alpha1) + (1/alpha2))\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 23,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# simulating one time step\n",
|
||||
"def simulate(C_t): \n",
|
||||
" C_t1 = np.zeros((grid_size['x'],grid_size['y']))\n",
|
||||
"\n",
|
||||
" # inner cells\n",
|
||||
" for i in range(1, grid_size['x']-1):\n",
|
||||
" for j in range(1, grid_size['y']-1):\n",
|
||||
" C_t1[i,j] = C_t[i,j] \\\n",
|
||||
" + max_stable_time_step/delta_x**2 * (alpha_interblock(alpha_x[i+1,j], alpha_x[i,j]) * C_t[i+1,j]\n",
|
||||
" - (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",
|
||||
" + alpha_interblock(alpha_x[i-1,j], alpha_x[i,j]) * C_t[i-1,j]) \\\n",
|
||||
" + max_stable_time_step/delta_y**2 * (alpha_interblock(alpha_y[i,j+1], alpha_y[i,j]) * C_t[i,j+1]\n",
|
||||
" - (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",
|
||||
" + alpha_interblock(alpha_y[i,j-1], alpha_y[i,j]) * C_t[i,j-1])\n",
|
||||
"\n",
|
||||
" return C_t1"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 27,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"[[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 4.93210938e+02 -6.85390625e+02 5.61357422e+02\n",
|
||||
" -3.21421875e+02 1.35512695e+02 -4.28554688e+01 1.01855469e+01\n",
|
||||
" -1.79687500e+00 2.28515625e-01 -1.95312500e-02 9.76562500e-04\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 -6.85390625e+02 9.41660156e+02 -7.56210938e+02\n",
|
||||
" 4.20468750e+02 -1.70039062e+02 5.07128906e+01 -1.10742188e+01\n",
|
||||
" 1.71875000e+00 -1.75781250e-01 9.76562500e-03 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 5.61357422e+02 -7.56210938e+02 5.86933594e+02\n",
|
||||
" -3.10078125e+02 1.16542969e+02 -3.12890625e+01 5.84472656e+00\n",
|
||||
" -7.03125000e-01 4.39453125e-02 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 -3.21421875e+02 4.20468750e+02 -3.10078125e+02\n",
|
||||
" 1.51593750e+02 -5.08593750e+01 1.15312500e+01 -1.64062500e+00\n",
|
||||
" 1.17187500e-01 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 1.35512695e+02 -1.70039062e+02 1.16542969e+02\n",
|
||||
" -5.08593750e+01 1.43554688e+01 -2.46093750e+00 2.05078125e-01\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 -4.28554688e+01 5.07128906e+01 -3.12890625e+01\n",
|
||||
" 1.15312500e+01 -2.46093750e+00 2.46093750e-01 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 1.01855469e+01 -1.10742188e+01 5.84472656e+00\n",
|
||||
" -1.64062500e+00 2.05078125e-01 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 -1.79687500e+00 1.71875000e+00 -7.03125000e-01\n",
|
||||
" 1.17187500e-01 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 2.28515625e-01 -1.75781250e-01 4.39453125e-02\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 -1.95312500e-02 9.76562500e-03 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 9.76562500e-04 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
|
||||
" [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
|
||||
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"for i in range(10):\n",
|
||||
" C_t = simulate(C_t)\n",
|
||||
"print(C_t)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 28,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"0.5\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"print(max_stable_time_step)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.10.1"
|
||||
},
|
||||
"orig_nbformat": 4
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 2
|
||||
}
|
||||
Loading…
x
Reference in New Issue
Block a user