From ec39d8f8f04b39d7aa5af233bd4af8590f88ef84 Mon Sep 17 00:00:00 2001
From: Lars Hubatsch <hubatsch@pks.mpg.de>
Date: Thu, 28 Nov 2019 22:23:31 +0100
Subject: [PATCH] Deleting simple Cahn Hilliard example. First trial Flory
Huggins with many terms (simple substitution of y=laplace(phi_tot) instead of
the entire chemical potential) still doesn't work properply. For now
continuing with amended Cahn Hilliard which accounts for Flory Huggins free
energy. The other Flory Huggins code probably has a coding/fenics issue I
don't see.
---
Fenics_Cahn_Hilliard.ipynb | 122 ----------------------------------
Fenics_FloryHugg_PhiTot.ipynb | 23 ++++---
2 files changed, 12 insertions(+), 133 deletions(-)
delete mode 100644 Fenics_Cahn_Hilliard.ipynb
diff --git a/Fenics_Cahn_Hilliard.ipynb b/Fenics_Cahn_Hilliard.ipynb
deleted file mode 100644
index cb709ff..0000000
--- a/Fenics_Cahn_Hilliard.ipynb
+++ /dev/null
@@ -1,122 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# Standard Cahn-Hilliard Example that runs with fenics 2019.1\n",
- "# Examples can be found at https://bitbucket.org/fenics-project/dolfin/src/master/python/demo/documented/cahn-hilliard/demo_cahn-hilliard.py.rst#rst-header-id1\n",
- "# The resulting .pvd file can be opened using default settings in ParaView\n",
- "\n",
- "import random\n",
- "from dolfin import *\n",
- "# Class representing the intial conditions\n",
- "class InitialConditions(UserExpression):\n",
- " def __init__(self, **kwargs):\n",
- " random.seed(2 + MPI.rank(MPI.comm_world))\n",
- " super().__init__(**kwargs)\n",
- " def eval(self, values, x):\n",
- " if x[0] > 0.5:\n",
- "# values[0] = 0.63 + 0.02*(0.5 - random.random())\n",
- " values[0] = 0.6\n",
- " else:\n",
- " values[0] = 0.35 \n",
- " values[1] = 0.0\n",
- "# values[0] = 0.63 + 0.02*(0.5 - random.random())\n",
- " values[1] = 0.0\n",
- " def value_shape(self):\n",
- " return (2,)\n",
- "# Class for interfacing with the Newton solver\n",
- "class CahnHilliardEquation(NonlinearProblem):\n",
- " def __init__(self, a, L):\n",
- " NonlinearProblem.__init__(self)\n",
- " self.L = L\n",
- " self.a = a\n",
- " def F(self, b, x):\n",
- " assemble(self.L, tensor=b)\n",
- " def J(self, A, x):\n",
- " assemble(self.a, tensor=A)\n",
- "# Model parameters\n",
- "lmbda = 2.0e-02 # surface parameter\n",
- "dt = 5.0e-03 # time step\n",
- "theta = 0.5 # time stepping family, e.g. theta=1 -> backward Euler, theta=0.5 -> Crank-Nicolson\n",
- "# Form compiler options\n",
- "parameters[\"form_compiler\"][\"optimize\"] = True\n",
- "parameters[\"form_compiler\"][\"cpp_optimize\"] = True\n",
- "# Create mesh and build function space\n",
- "mesh = UnitSquareMesh.create(96, 3, CellType.Type.quadrilateral)\n",
- "P1 = FiniteElement(\"Lagrange\", mesh.ufl_cell(), 1)\n",
- "ME = FunctionSpace(mesh, P1*P1)\n",
- "# Define trial and test functions\n",
- "du = TrialFunction(ME)\n",
- "q, v = TestFunctions(ME)\n",
- "# Define functions\n",
- "u = Function(ME) # current solution\n",
- "u0 = Function(ME) # solution from previous converged step\n",
- "\n",
- "# Split mixed functions\n",
- "dc, dmu = split(du)\n",
- "c, mu = split(u)\n",
- "c0, mu0 = split(u0)\n",
- "# Create intial conditions and interpolate\n",
- "u_init = InitialConditions(degree=1)\n",
- "u.interpolate(u_init)\n",
- "u0.interpolate(u_init)\n",
- "# Compute the chemical potential df/dc\n",
- "c = variable(c)\n",
- "# f = 100*c**2*(1-c)**2\n",
- "# dfdc = diff(f, c)\n",
- "X = 2.2\n",
- "dfdc = ln(c/(1-c))+(1-2*X*c)\n",
- "# mu_(n+theta)\n",
- "mu_mid = (1.0-theta)*mu0 + theta*mu\n",
- "# Weak statement of the equations\n",
- "L0 = c*q*dx - c0*q*dx + dt*c*(1-c)*dot(grad(mu_mid), grad(q))*dx\n",
- "L1 = mu*v*dx - dfdc*v*dx - lmbda*dot(grad(c), grad(v))*dx\n",
- "L = L0 + L1\n",
- "# Compute directional derivative about u in the direction of du (Jacobian)\n",
- "a = derivative(L, u, du)\n",
- "# Create nonlinear problem and Newton solver\n",
- "problem = CahnHilliardEquation(a, L)\n",
- "solver = NewtonSolver()\n",
- "solver.parameters[\"linear_solver\"] = \"lu\"\n",
- "solver.parameters[\"convergence_criterion\"] = \"incremental\"\n",
- "solver.parameters[\"relative_tolerance\"] = 1e-6\n",
- "# Output file\n",
- "file = File(\"output.pvd\", \"compressed\")\n",
- "\n",
- "# Step in time\n",
- "t = 0.0\n",
- "T = 5000*dt\n",
- "while (t < T):\n",
- " t += dt\n",
- " u0.vector()[:] = u.vector()\n",
- " solver.solve(problem, u.vector())\n",
- " file << (u.split()[0], t)"
- ]
- }
- ],
- "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": "3.7.3"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}
diff --git a/Fenics_FloryHugg_PhiTot.ipynb b/Fenics_FloryHugg_PhiTot.ipynb
index ab2a465..9c3710e 100644
--- a/Fenics_FloryHugg_PhiTot.ipynb
+++ b/Fenics_FloryHugg_PhiTot.ipynb
@@ -19,9 +19,10 @@
" super().__init__(**kwargs)\n",
" def eval(self, values, x):\n",
" if x[0] > 0.5:\n",
- " values[0] = 0.63 + 0.02*(0.5 - random.random())\n",
+ "# values[0] = 0.63 + 0.02*(0.5 - random.random())\n",
+ " values[0] = 0.6\n",
" else:\n",
- " values[0] = 0.4 \n",
+ " values[0] = 0.35 \n",
" values[1] = 0.0\n",
" def value_shape(self):\n",
" return (2,)\n",
@@ -36,16 +37,16 @@
" def J(self, A, x):\n",
" assemble(self.a, tensor=A)\n",
"# Model parameters\n",
- "dt = 5.0e-10 # time step\n",
+ "dt = 5.0e-11 # time step\n",
"theta = 0.5 # time stepping family, e.g. theta=1 -> backward Euler, theta=0.5 -> Crank-Nicolson\n",
"kBTG0 = 1.0e-6\n",
- "X = 3.5\n",
+ "X = 2.2\n",
"kappa = 2\n",
"# Form compiler options\n",
"parameters[\"form_compiler\"][\"optimize\"] = True\n",
"parameters[\"form_compiler\"][\"cpp_optimize\"] = True\n",
"# Create mesh and build function space\n",
- "mesh = UnitSquareMesh.create(96, 1, CellType.Type.quadrilateral)\n",
+ "mesh = UnitSquareMesh.create(96, 3, CellType.Type.quadrilateral)\n",
"P1 = FiniteElement(\"Lagrange\", mesh.ufl_cell(), 1)\n",
"ME = FunctionSpace(mesh, P1*P1)\n",
"# Define trial and test functions\n",
@@ -74,9 +75,9 @@
"# time and therefore doesn't need discretization in time, check this is true with Chris!\n",
"# In particular the c_mid in L0!\n",
"L0 = (1/kBTG0*(c*q*dx - c0*q*dx) - dt*((1+2*X*c_mid)*mu_mid- 2*X*dot(grad(mu_mid), grad(mu_mid))\n",
- " +2*X*(2*c_mid*dot(grad(c_mid), grad(c_mid)) + c_mid**2*mu_mid) \n",
- " -kappa*(dot(grad(c_mid), grad(mu_mid)) - 2*c_mid*dot(grad(c_mid), grad(mu_mid))))*q*dx\n",
- " -kappa*(c_mid**2*dot(grad(mu_mid), grad(q))+2*c_mid*q*dot(grad(mu_mid), grad(c_mid)))*dx)\n",
+ " +2*X*(2*c_mid*dot(grad(c_mid), grad(c_mid)) + c_mid**2*mu_mid) \n",
+ " -kappa*(dot(grad(c_mid), grad(mu_mid)) - 2*c_mid*dot(grad(c_mid), grad(mu_mid))))*q*dx\n",
+ " -dt*kappa*(c_mid**2*dot(grad(mu_mid), grad(q))+2*c_mid*q*dot(grad(mu_mid), grad(c_mid)))*dx)\n",
"# L1 = mu*v*dx - dfdc*v*dx - lmbda*dot(grad(c), grad(v))*dx\n",
"L1 = mu*v*dx + dot(grad(c), grad(v))*dx\n",
"L = L0 + L1\n",
@@ -93,12 +94,12 @@
"\n",
"# Step in time\n",
"t = 0.0\n",
- "T = 200*dt\n",
+ "T = 2000*dt\n",
"while (t < T):\n",
- " t += dt\n",
" u0.vector()[:] = u.vector()\n",
" solver.solve(problem, u.vector())\n",
- " file << (u.split()[0], t)"
+ " file << (u.split()[0], t)\n",
+ " t += dt"
]
}
],
--
GitLab