From d74d736a735e6fe7b206f6bdb4550ef807f2673b Mon Sep 17 00:00:00 2001
From: Lars Hubatsch <hubatsch@pks.mpg.de>
Date: Fri, 18 Sep 2020 00:12:01 +0200
Subject: [PATCH] Change cell order. Works OK for small times.
Probably need proper dependence on phi_tot instead of direct dependence on x.
---
FloryHugg_DiffUnbleached.ipynb | 124 +++++++++++++++++----------------
1 file changed, 64 insertions(+), 60 deletions(-)
diff --git a/FloryHugg_DiffUnbleached.ipynb b/FloryHugg_DiffUnbleached.ipynb
index f9d2427..d631829 100644
--- a/FloryHugg_DiffUnbleached.ipynb
+++ b/FloryHugg_DiffUnbleached.ipynb
@@ -16,7 +16,7 @@
"# domain = ms.Sphere(df.Point(0, 0, 0), 1.0)\n",
"# mesh = ms.generate_mesh(domain, 50)\n",
"mesh = df.UnitIntervalMesh(10000)\n",
- "dt = 0.0001\n",
+ "dt = 0.001\n",
"\n",
"F = df.FunctionSpace(mesh, 'CG', 1)"
]
@@ -33,28 +33,28 @@
" X = df.SpatialCoordinate(mesh)\n",
"# X.interpolate(df.Expression('x[0]', degree=1))\n",
" # Weak form 1D:\n",
- "# form = ((df.inner((c-c0)/dt, tc) +\n",
- "# df.inner(df.grad(c), df.grad((1-c_tot)/Ga0*tc))) -\n",
- "# df.inner(df.grad(c_tot), df.grad((1-c_tot)/Ga0/c_tot*c*tc))-\n",
- "# tc*df.inner(df.grad(c), df.grad((1-c_tot)/Ga0))+\n",
- "# tc*df.inner(df.grad(c_tot), df.grad((1-c_tot)/c_tot*c/Ga0))) * df.dx\n",
+ " form = ((df.inner((c-c0)/dt, tc) +\n",
+ " df.inner(df.grad(c), df.grad((1-c_tot)*Ga0*tc))) -\n",
+ " df.inner(df.grad(c_tot), df.grad((1-c_tot)*Ga0/c_tot*c*tc))-\n",
+ " tc*df.inner(df.grad(c), df.grad((1-c_tot)*Ga0))+\n",
+ " tc*df.inner(df.grad(c_tot), df.grad((1-c_tot)/c_tot*c*Ga0))) * df.dx\n",
" \n",
"# # Weak form radial symmetry:\n",
- " form = ((df.inner((c-c0)/dt, tc*X[0]*X[0]) +\n",
- " df.inner(df.grad(c), df.grad((1-c_tot)*Ga0*tc*X[0]*X[0]))) -\n",
- " df.inner(df.grad(c_tot), df.grad((1-c_tot)*Ga0/c_tot*c*tc*X[0]*X[0]))-\n",
- " tc*df.inner(df.grad(c), df.grad((1-c_tot)*Ga0*X[0]*X[0]))+\n",
- " tc*df.inner(df.grad(c_tot), df.grad((1-c_tot)/c_tot*c*Ga0*X[0]*X[0]))-\n",
- " (1-c_tot)*Ga0*2*X[0]*c.dx(0)*tc+\n",
- " (1-c_tot)*Ga0/c_tot*c*2*X[0]*c_tot.dx(0)*tc) * df.dx\n",
+ "# form = ((df.inner((c-c0)/dt, tc*X[0]*X[0]) +\n",
+ "# df.inner(df.grad(c), df.grad((1-c_tot)*Ga0*tc*X[0]*X[0]))) -\n",
+ "# df.inner(df.grad(c_tot), df.grad((1-c_tot)*Ga0/c_tot*c*tc*X[0]*X[0]))-\n",
+ "# tc*df.inner(df.grad(c), df.grad((1-c_tot)*Ga0*X[0]*X[0]))+\n",
+ "# tc*df.inner(df.grad(c_tot), df.grad((1-c_tot)/c_tot*c*Ga0*X[0]*X[0]))-\n",
+ "# (1-c_tot)*Ga0*2*X[0]*c.dx(0)*tc+\n",
+ "# (1-c_tot)*Ga0/c_tot*c*2*X[0]*c_tot.dx(0)*tc) * df.dx\n",
" # Weak form radial symmetry:\n",
"# form = ((df.inner((c-c0)/dt, tc*X[0]*X[0]) +\n",
- "# df.inner(df.grad(c), df.grad((1-c_tot+a*c_tot*c_tot)*tc*X[0]*X[0]))) -\n",
- "# df.inner(df.grad(c_tot), df.grad((1-c_tot+a*c_tot*c_tot)/c_tot*c*tc*X[0]*X[0]))-\n",
- "# tc*df.inner(df.grad(c), df.grad((1-c_tot+a*c_tot*c_tot)*X[0]*X[0]))+\n",
- "# tc*df.inner(df.grad(c_tot), df.grad((1-c_tot+a*c_tot*c_tot)/c_tot*c*X[0]*X[0]))-\n",
- "# (1-c_tot+a*c_tot*c_tot)*2*X[0]*c.dx(0)*tc+\n",
- "# (1-c_tot+a*c_tot*c_tot)/c_tot*c*2*X[0]*c_tot.dx(0)*tc) * df.dx\n",
+ "# df.inner(df.grad(c), df.grad((1-c_tot+Ga0*c_tot*c_tot)*tc*X[0]*X[0]))) -\n",
+ "# df.inner(df.grad(c_tot), df.grad((1-c_tot+Ga0*c_tot*c_tot)/c_tot*c*tc*X[0]*X[0]))-\n",
+ "# tc*df.inner(df.grad(c), df.grad((1-c_tot+Ga0*c_tot*c_tot)*X[0]*X[0]))+\n",
+ "# tc*df.inner(df.grad(c_tot), df.grad((1-c_tot+Ga0*c_tot*c_tot)/c_tot*c*X[0]*X[0]))-\n",
+ "# (1-c_tot+Ga0*c_tot*c_tot)*2*X[0]*c.dx(0)*tc+\n",
+ "# (1-c_tot+Ga0*c_tot*c_tot)/c_tot*c*2*X[0]*c_tot.dx(0)*tc) * df.dx\n",
" \n",
" t = 0\n",
" # Solve in time\n",
@@ -71,7 +71,11 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "jupyter": {
+ "source_hidden": true
+ }
+ },
"outputs": [],
"source": [
"# Interpolate c_tot and initial conditions\n",
@@ -110,6 +114,42 @@
"Ga0_9.interpolate(df.Expression('1', degree=1))"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "p1_i = 0.9\n",
+ "p1_o = 0.1\n",
+ "p2_i = 0.8\n",
+ "p2_o = 0.2\n",
+ "a1 = 0\n",
+ "\n",
+ "def p_tot(p_i, p_o):\n",
+ " return str(p_i-p_o)+'*(-0.5*tanh(3500*(x[0]-0.1))+0.5)+'+str(p_o)\n",
+ "\n",
+ "ct_1 = df.Function(F)\n",
+ "ct_2 = df.Function(F)\n",
+ "c0_1 = df.Function(F)\n",
+ "c0_2 = df.Function(F)\n",
+ "g_1 = df.Function(F)\n",
+ "g_2 = df.Function(F)\n",
+ "\n",
+ "ct_1.interpolate(df.Expression(p_tot(p1_i, p1_o), degree=1))\n",
+ "ct_2.interpolate(df.Expression(p_tot(p2_i, p2_o), degree=1))\n",
+ "P1 = c_tot1(0)/c_tot1(1)\n",
+ "P2 = c_tot2(0)/c_tot2(1)\n",
+ "\n",
+ "g_1.interpolate(df.Expression('1', degree=1))\n",
+ "g_2.interpolate(df.Expression(p_tot(p1_o/p2_o, 1), degree=1))\n",
+ "D_out1 = 1-c_tot1(1)\n",
+ "a = (P2*D_out1/P1-1+p2_o)/p2_o**2\n",
+ "\n",
+ "c0_1.interpolate(df.Expression('x[0]<0.1 ? 0 :'+p_tot(p1_i, p1_o), degree=1))\n",
+ "c0_2.interpolate(df.Expression('x[0]<0.1 ? 0 :'+p_tot(p2_i, p2_o), degree=1))"
+ ]
+ },
{
"cell_type": "code",
"execution_count": null,
@@ -133,9 +173,9 @@
"outputs": [],
"source": [
"# 1D:\n",
- "plt.plot(np.linspace(0, 1, 10000), [1.31*c0_1([x]) for x in np.linspace(0, 1, 10000)])\n",
+ "plt.plot(np.linspace(0, 1, 10000), [1.465*c0_1([x]) for x in np.linspace(0, 1, 10000)])\n",
"plt.plot(np.linspace(0, 1, 10000), [c0_2([x]) for x in np.linspace(0, 1, 10000)])\n",
- "plt.xlim(0.06, 0.125)\n",
+ "plt.xlim(0.0, 0.125)\n",
"# plt.ylim(0, 0.3)\n",
"# 3D:\n",
"# plt.plot(np.linspace(0, 0.5, 1000), [c0([x, 0, 0]) for x in np.linspace(0, 0.5, 1000)])"
@@ -166,44 +206,8 @@
"metadata": {},
"outputs": [],
"source": [
- "p1_i = 0.9\n",
- "p1_o = 0.1\n",
- "p2_i = 0.8\n",
- "p2_o = 0.2\n",
- "a1 = 0\n",
- "\n",
- "def p_tot(p_i, p_o):\n",
- " return str(p_i-p_o)+'*(-0.5*tanh(350000*(x[0]-0.1))+0.5)+'+str(p_o)\n",
- "\n",
- "ct_1 = df.Function(F)\n",
- "ct_2 = df.Function(F)\n",
- "c0_1 = df.Function(F)\n",
- "c0_2 = df.Function(F)\n",
- "g_1 = df.Function(F)\n",
- "g_2 = df.Function(F)\n",
- "\n",
- "ct_1.interpolate(df.Expression(p_tot(p1_i, p1_o), degree=1))\n",
- "ct_2.interpolate(df.Expression(p_tot(p2_i, p2_o), degree=1))\n",
- "P1 = c_tot1(0)/c_tot1(1)\n",
- "P2 = c_tot2(0)/c_tot2(1)\n",
- "\n",
- "g_1.interpolate(df.Expression('1', degree=1))\n",
- "g_2.interpolate(df.Expression(p_tot(p1_o/p2_o, p1_i/p2_i), degree=1))\n",
- "D_out1 = 1-c_tot1(1)\n",
- "a = (P2*D_out1/P1-1+p2_o)/p2_o**2\n",
- "\n",
- "c0_1.interpolate(df.Expression('x[0]<0.1 ? 0 :'+p_tot(p1_i, p1_o), degree=1))\n",
- "c0_2.interpolate(df.Expression('x[0]<0.1 ? 0 :'+p_tot(p2_i, p2_o), degree=1))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "plt.plot(np.linspace(0, 1, 1000), [ct_1([x]) for x in np.linspace(0, 1, 1000)])\n",
- "plt.plot(np.linspace(0, 1, 1000), [ct_2([x]) for x in np.linspace(0, 1, 1000)])\n",
+ "plt.plot(np.linspace(0, 1, 1000), [(1-ct_1([x]))*ct_1([x]) for x in np.linspace(0, 1, 1000)])\n",
+ "plt.plot(np.linspace(0, 1, 1000), [(1-ct_2([x]))*g_2([x]) for x in np.linspace(0, 1, 1000)])\n",
"plt.show()\n",
"\n",
"plt.plot(np.linspace(0, 1, 1000), [g_2([x]) for x in np.linspace(0, 1, 1000)])\n",
--
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