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@guyer
Last active July 14, 2016 16:17
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Jupyter notebooks illustrating different ways to couple two equations over different spatial domains in FiPy
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Implementation of coupled boundary condition problem raised on the FiPy mailing list: http://comments.gmane.org/gmane.comp.python.fipy/4197\n",
"\n",
"This implemantation defines PDE1 and PDE2 on a Grid2D and uses the values of one to constrain the other. Even though PDE1 is defined over a 2D domain, its values are only coupled to PDE2 at the top boundary. \n",
"\n",
"It might be possible to formally couple the equations, but that wasn't immediately working for me."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from matplotlib import pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import fipy as fp"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"nx = 10\n",
"ny = 10\n",
"Lx = 1.\n",
"Ly = 1."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"S = 1."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def f(w, a):\n",
" return w**3 * a"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"mesh = fp.Grid2D(nx=nx, ny=ny, Lx=Lx, Ly=Ly)\n",
"\n",
"x, y = mesh.cellCenters\n",
"X, Y = mesh.faceCenters\n",
"\n",
"a = fp.CellVariable(mesh=mesh)\n",
"B = fp.CellVariable(mesh=mesh, hasOld=True)\n",
"\n",
"w = B\n",
"\n",
"eq1 = fp.DiffusionTerm(coeff=[[[S, 0.], [0., 0.]]]) == f(w, a)\n",
"\n",
"a.constrain(0, where=X == 0)\n",
"a.faceGrad.constrain(1, where=X == 1)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"D = 1."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def g(w, a):\n",
" return w+a"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"eq2 = fp.TransientTerm() == fp.DiffusionTerm(coeff=[[[0, 0], [0, D]]])\n",
"\n",
"B.constrain(0, where=Y == 0)\n",
"B.faceGrad.constrain(g(w.faceValue, a.faceValue), where=Y == 1)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"steps = 10\n",
"dt = 1."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
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GjM6TXO9jwNeARwucy8z62HamtbW06UxgZUQcDHwn2663DTg9In4DWAh8tFFl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\n8jQzy8HJ08wsBydPM7McnDzNzHL4/xpoNLTz2b/jAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1118e3210>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(6, 5))\n",
"ax1 = fig.add_axes((0.15, 0.9, 0.7, 0.1))\n",
"ax2 = fig.add_axes((0.15, 0.1, 0.7, 0.7), sharex=ax1)\n",
"viewer1 = fp.Viewer(vars=a, axes=ax1, xmin=0., xmax=1.)\n",
"viewer2 = fp.Viewer(vars=B, axes=ax2, xmin=0., xmax=1., ymin=0., ymax=1.)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"a.value = 0.\n",
"B.value = 0."
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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KZ/yPWdnVUIOrjJlfBOBFzu85xv0yAA/vTe8i4ejrAB4ifhN7z3uea7Y+QZaW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\nHHfZZZddDNnhuMsuu+xiyP8H4B00y517hLQAAAAASUVORK5CYII=\n"
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0x1113a0050>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for step in range(steps):\n",
" B.updateOld()\n",
" res1 = res2 = 1e6\n",
" while res1 > 1e-3 and res2 > 1e-3:\n",
" res1 = eq1.sweep(a)\n",
" res2 = eq2.sweep(B, dt=dt)\n",
" \n",
" viewer1.plot()\n",
" viewer2.plot()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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