{ "cells": [ { "cell_type": "markdown", "id": "e601b878", "metadata": {}, "source": [ "# Viscoelastic Oldroyd-B model -- axi-symmetric Couette flow\n", "***" ] }, { "cell_type": "markdown", "id": "6552f774", "metadata": {}, "source": [ "## Introduction to viscoelastic Oldroyd-B model\n", "We deal with the viscoelastic Oldroyd-B model (Oldroyd, 1950). It is a model for material that exhibits both viscous and elastic behavior. For simplicity, we can imagine it in one dimension using the mechanical analogs: a linear spring and a linear dashpot, see the Figure below.

\n", "

\n", "\n", "
\n", "\n", "The linear spring represents an elastic material whose relation between the one-dimensional stress $\\sigma$ and one-dimensional strain $\\varepsilon$ reads\n", "\\begin{equation}\n", "\\sigma=G \\varepsilon,\n", "\\end{equation}\n", "where $G$ is the elastic modulus of the spring. The linear dashpot represents the Newtonian fluid with the relation\n", "\\begin{equation}\n", "\\sigma=\\mu\\dot{\\varepsilon},\n", "\\end{equation}\n", "where $\\mu$ is the fluid viscosity.\n", "\n", "Thus, if we assume that all points of the material are dashpots, we have a Newtonian fluid; if we assume that all points are springs, we obtain an elastic solid. In case of viscoelastic fluids we create a mixture of springs and dashpots. The Oldroyd mechanical analog consists of one spring and one dashpot connected to series (called Maxwell analog), and an additional dashpot that is attached in parallel, see the Figure below.

\n", "

\n", "\n", "
\n", "\n", "To get the relation between the total stress $\\sigma$ and the total strain $\\varepsilon$, we realize that\n", "\\begin{align}\n", "\\sigma&=\\sigma_{\\rm D_2} + \\sigma_{\\rm M},\\qquad&{\\rm and}&&\\qquad \\varepsilon&=\\varepsilon_{\\rm D_2}=\\varepsilon_{\\rm M},\\\\\n", "\\sigma_{\\rm M}&=\\sigma_{\\rm D_1}=\\sigma_{\\rm S},\\qquad&{\\rm and}&&\\qquad\\varepsilon_{\\rm M}&=\\varepsilon_{\\rm D_1}+\\varepsilon_{\\rm S}.\n", "\\end{align}\n", "By straightforward manipulation we get the relation for the Maxwell analog, i.e.\n", "\\begin{align}\n", "\\dot{\\varepsilon}_{\\rm M}&=\\dot{\\varepsilon}_{\\rm D_1}+\\dot{\\varepsilon}_{\\rm S}\\nonumber\\\\\n", "&=\\frac{\\sigma_{\\rm D_1}}{\\mu}+\\frac{\\dot{\\sigma}_{\\rm S}}{G}\\\\\n", "&=\\frac{\\sigma_{\\rm M}}{\\mu_1}+\\frac{\\dot{\\sigma}_{\\rm M}}{G},\\nonumber\n", "\\end{align}\n", "or we can write it a slightly different way\n", "\\begin{equation}\n", "\\dot{\\sigma}_{\\rm M}+\\frac{G}{\\mu_1}\\sigma_{\\rm M}=G\\dot{\\varepsilon}_{\\rm M}.\n", "\\end{equation}\n", "Then, the stress-strain relation for the Oldroyd one-dimensional analog simply reads\n", "\\begin{align}\n", "\\sigma=\\mu_2\\dot{\\varepsilon}+\\sigma_{\\rm M},\\\\\n", "\\dot{\\sigma}_{\\rm M}+\\frac{G}{\\mu_1}\\sigma_{\\rm M}&=G\\dot{\\varepsilon}_{\\rm M}.\n", "\\end{align}\n", "However, we obtained only the relation between the stress and strain in one dimension. The journey to a fully three-dimensional model is long and it is beyond the scope of this FEniCS tutorial. In short, in the fully three-dimensional Oldroyd-B model, the one-dimensional stress $\\sigma$ is replaced by the Cauchy stress $\\mathbb{T}$, $\\dot{\\varepsilon}$ by the symmetric part of the velocity gradient $\\mathbb{D}$ and the simple derivative by the objective upper-convected Oldroyd derivative that transforms correctly under the change of observer. The Cauchy stress tensor $\\mathbb{T}$ for the Oldroyd-B model reads\n", "\\begin{align}\n", "\\mathbb{T}&=-p\\mathbb{I}+2\\mu_2\\mathbb{D}+\\mathbb{A},\\\\\n", "\\frac{\\partial \\mathbb{A}}{\\partial t}+{\\bf v}\\cdot\\nabla\\mathbb{A}-(\\nabla{\\bf v})\\mathbb{A}-\\mathbb{A}(\\nabla{\\bf v})^{\\rm T}+\\frac{G}{\\mu_1}\\mathbb{A}&=2G\\mathbb{D}.\n", "\\end{align}\n", "\n", "Finally, the full set of governing equations for the Oldroyd-B model read\n", "\\begin{align}\n", "{\\rm div}\\,{\\bf v}&=0,\\\\\n", "\\rho\\left(\\frac{\\partial{\\bf v}}{\\partial t}+({\\bf v}\\cdot\\nabla){\\bf v}\\right)&={\\rm div}\\,\\mathbb{T},\\quad\n", "\\mathbb{T}=-p\\mathbb{I}+2\\mu_2\\mathbb{D}+\\mathbb{A},\\\\\n", "\\frac{\\partial \\mathbb{A}}{\\partial t}+{\\bf v}\\cdot\\nabla\\mathbb{A}-(\\nabla{\\bf v})\\mathbb{A}-\\mathbb{A}(\\nabla{\\bf v})^{\\rm T}+\\frac{G}{\\mu_1}\\mathbb{A}&=2G\\mathbb{D}.\n", "\\end{align}\n", "\n", "Very often, the equations are rewritten in the form where $\\mathbb{A}=G(\\mathbb{B}-\\mathbb{I})$. The model then transforms to\n", "\\begin{align}\n", "{\\rm div}\\,{\\bf v}&=0,\\\\\n", "\\rho\\left(\\frac{\\partial{\\bf v}}{\\partial t}+({\\bf v}\\cdot\\nabla){\\bf v}\\right)&={\\rm div}\\,\\mathbb{T},\\quad\n", "\\mathbb{T}=-p\\mathbb{I}+2\\mu_2\\mathbb{D}+G(\\mathbb{B}-\\mathbb{I}),\\\\\n", "\\frac{\\partial \\mathbb{B}}{\\partial t}+{\\bf v}\\cdot\\nabla\\mathbb{B}-(\\nabla{\\bf v})\\mathbb{B}-\\mathbb{B}(\\nabla{\\bf v})^{\\rm T}+\\frac{G}{\\mu_1}(\\mathbb{B}-\\mathbb{I})&=\\mathbb{O}.\n", "\\end{align}" ] }, { "cell_type": "markdown", "id": "3d92a1d2", "metadata": {}, "source": [ "## Problem description\n", "\n", "We test our finite element implementation on a problem for which we have a non-trivial analytical solution -- the problem of axi-symmetric steady Couette flow. The domain $\\Omega$ is bordered with two concentric circles, radius of the inner one is 1 m, radius of\n", "the outer one is 2 m, the material flows inside these two circles and fully sticks to both boundaries. The inner circle is fixed and does not move, the outer one rotates with constant angular velocity $\\omega = 0.5$ rad s$^{-1}$, thus the fluid rotates with it. The problem is depicted in the Figure below.

\n", "

\n", "\n", "
\n", "\n", "To obtain the analytical solution, we employ the polar coordinates, we assume that all unknowns $p, {\\bf v}, \\mathbb{B}$ depend only on the radial coordinate $r$ and the fluid flows only in the direction of rotation, i.e.\n", "\\begin{equation}\n", "{\\bf v}=(0, v_{\\varphi}(r)).\n", "\\end{equation}\n", "If we fix the pressure $p=0$ at the inner circle, the analytical solution reads\n", "\\begin{align}\n", "v_{\\varphi}&=\\frac23\\left(r-\\frac{1}{r}\\right),\\\\\n", "p&=\\frac{4\\rho}{9}\\left(\\frac{r^2}{2}-2\\ln r - \\frac{1}{2r^2}\\right)+\\frac{8}{9}\\left(\\frac{\\mu_1^2}{G r^4}-1\\right),\\\\\n", "B_{rr}&=1,\\quad B_{r\\varphi}=\\frac{4\\mu_1}{3G r^2},\\quad B_{\\varphi\\varphi}=1+\\frac{32\\mu_1^2}{9G^2 r^4}.\n", "\\end{align}" ] }, { "cell_type": "markdown", "id": "2afee10d", "metadata": {}, "source": [ "## Weak formulation\n", "\n", "Since we are interested in the steady solution, we omit the time derivatives, test the corresponding equations by the test arbitrary functions $(q, {\\bf q}, \\mathbb{Q})$, integrate over $\\Omega$ and use the divergence theorem\n", "\\begin{align}\n", "&\\int_\\Omega \\mathrm{div}\\,\\mathbf{v} \\, q\\; \\mathrm{d}\\mathbf{x} = 0,\\\\\n", "&\\int_\\Omega (\\rho\\mathbf{v}\\cdot\\nabla\\mathbf{v})\\cdot\\mathbf{q}\\; \\mathrm{d}\\mathbf{x} + \\int_\\Omega \\mathbb{T}\\cdot\\nabla\\mathbf{q}\\; \\mathrm{d}\\mathbf{x} = 0,\\\\\n", "&\\int_\\Omega \\left({\\bf v}\\cdot\\nabla\\mathbb{B}-(\\nabla{\\bf v})\\mathbb{B}-\\mathbb{B}(\\nabla{\\bf v})^{\\rm T}+\\frac{G}{\\mu_1}(\\mathbb{B}-\\mathbb{I})\\right)\\cdot\\mathbb{Q}=0,\n", "\\end{align}\n", "where\n", "\\begin{equation}\n", "\\mathbb{T}=-p\\mathbb{I}+2\\mu_2\\mathbb{D}+G(\\mathbb{B}-\\mathbb{I}).\n", "\\end{equation}\n", "\n", "Here, we imposed that $\\mathbf{v}$ vanishes on the Dirichlet boundaries $\\Gamma_\\mathrm{in}$, $\\Gamma_\\mathrm{out}$.\n", "\n", "This non-linear problem is now solved using the FEniCS and compared to the analytical solution." ] }, { "cell_type": "markdown", "id": "ce0eb767", "metadata": {}, "source": [ "## FEniCS implementation" ] }, { "cell_type": "markdown", "id": "341ee625", "metadata": {}, "source": [ "Import **dolfin** (FEniCS backend), **matplotlib.pyplot** (for plots), **numpy** (for arrays), **mshr** (for meshing) and **time** (for time benchmarking)." ] }, { "cell_type": "code", "execution_count": 1, "id": "edab3916", "metadata": {}, "outputs": [], "source": [ "import dolfin as df\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import mshr\n", "from time import time" ] }, { "cell_type": "markdown", "id": "34b4ab07", "metadata": {}, "source": [ "Create mesh." ] }, { "cell_type": "code", "execution_count": 2, "id": "9ef9e39b", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "R1 = 1.0 # Radius R1\n", "R2 = 2.0 # Radius R2\n", "geometry = mshr.Circle(df.Point(0.0, 0.0), R2, 720) - mshr.Circle(df.Point(0.0, 0.0), R1, 720)\n", "\n", "mesh = mshr.generate_mesh(geometry, 75)\n", "mesh.init() \n", "df.plot(mesh)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "16e188ec", "metadata": {}, "source": [ "Identify boundaries." ] }, { "cell_type": "code", "execution_count": 3, "id": "459e737f", "metadata": {}, "outputs": [], "source": [ "# define boundary as a class\n", "class Inner(df.SubDomain):\n", " def inside(self, x, on_boundary):\n", " return on_boundary and x[0]*x[0]+x[1]*x[1]R2*R2-1.0e-3\n", "\n", "outer = Outer()\n", "\n", "# mark boundary parts\n", "bndry = df.MeshFunction('size_t', mesh, mesh.topology().dim()-1, 0)\n", "inner.mark(bndry, 1)\n", "outer.mark(bndry, 2)" ] }, { "cell_type": "markdown", "id": "f0327255", "metadata": {}, "source": [ "Define mixed function space for pressure $p$, velocity $\\mathbf{v}$ and extra stress tensor $\\mathbb{B}$. In this example, we use inf-sup stable Taylor-Hood elements for velocity and pressure, which are quadratic in velocity and linear in pressure; and linear in extra stress tensor." ] }, { "cell_type": "code", "execution_count": 4, "id": "abaf713b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Problem size: 115896\n" ] } ], "source": [ "Ev = df.VectorElement(\"CG\", mesh.ufl_cell(), 2) # 2 = quadratic elements\n", "Ep = df.FiniteElement(\"CG\", mesh.ufl_cell(), 1) # 1 = linear elements\n", "E = df.MixedElement([Ev, Ep, Ep, Ep, Ep])\n", "W = df.FunctionSpace(mesh, E)\n", "print(\"Problem size: {0:d}\".format(W.dim())) " ] }, { "cell_type": "markdown", "id": "ca265b43", "metadata": {}, "source": [ "Declare boundary conditions." ] }, { "cell_type": "code", "execution_count": 5, "id": "6c7881e2", "metadata": {}, "outputs": [], "source": [ "outervel = df.Expression((\"-Omega*x[1]\", \"Omega*x[0]\"), Omega=0.5, degree=1)\n", "innervel = df.Expression((\"-Omega*x[1]\", \"Omega*x[0]\"), Omega=0.0, degree=1)\n", "\n", "bc_inner = df.DirichletBC(W.sub(0), innervel, bndry, 1) #inner radius\n", "bc_outer = df.DirichletBC(W.sub(0), outervel, bndry, 2) #outer radius\n", "bcp = df.DirichletBC(W.sub(4), df.Constant(0.0), \"near(x[0],1.0) && near(x[1],0.0)\", method=\"pointwise\") #Fix the pressure at one point\n", "\n", "bcs = [bc_outer, bc_inner, bcp] " ] }, { "cell_type": "markdown", "id": "888b0f97", "metadata": {}, "source": [ "Write the weak form." ] }, { "cell_type": "code", "execution_count": 6, "id": "14c1f82c", "metadata": {}, "outputs": [], "source": [ "rho = df.Constant(1.0)\n", "mu1 = df.Constant(1.0)\n", "mu2 = df.Constant(1.0)\n", "G = df.Constant(1.0)\n", "\n", "v_, b11_, b12_, b22_, p_ = df.TestFunctions(W)\n", "w = df.Function(W)\n", "v, b11, b12, b22, p = df.split(w)\n", "\n", "B_ = df.as_tensor([[b11_,b12_],[b12_,b22_]])\n", "B = df.as_tensor([[b11,b12],[b12,b22]])\n", "\n", "I = df.Identity(mesh.geometry().dim())\n", "L = df.grad(v)\n", "D = 0.5*(L + L.T)\n", "matderv = df.grad(v)*v\n", "T = -p*I + 2.0*mu2*D + G*(B-I)\n", "oldroydderB = B.dx(0)*v[0] + B.dx(1)*v[1] - L*B - B*(L.T)\n", "\n", "Eq1 = df.div(v)*p_*df.dx\n", "Eq2 = df.inner(rho*matderv, v_)*df.dx + df.inner(T, df.grad(v_))*df.dx\n", "Eq3 = df.inner(oldroydderB, B_)*df.dx + mu1/G*df.inner(B - I, B_)*df.dx\n", "\n", "Eq = Eq1 + Eq2 + Eq3 " ] }, { "cell_type": "markdown", "id": "6339c0c4", "metadata": {}, "source": [ "Solve the non-linear problem using Newton solver." ] }, { "cell_type": "code", "execution_count": 7, "id": "5a6aef98", "metadata": {}, "outputs": [], "source": [ "problem=df.NonlinearVariationalProblem(Eq,w,bcs,df.derivative(Eq,w))\n", "solver=df.NonlinearVariationalSolver(problem)" ] }, { "cell_type": "markdown", "id": "8c53fd05", "metadata": {}, "source": [ "Solve the linear problem using *mumps* direct sparse linear solver." ] }, { "cell_type": "code", "execution_count": 8, "id": "e6b83524", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving nonlinear variational problem.\n", "Elapsed time = 15.030437707901001\n", " Newton iteration 0: r (abs) = 8.512e+01 (tol = 5.000e-09) r (rel) = 1.000e+00 (tol = 5.000e-09)\n", " Newton iteration 1: r (abs) = 1.293e-01 (tol = 5.000e-09) r (rel) = 1.519e-03 (tol = 5.000e-09)\n", " Newton iteration 2: r (abs) = 6.485e-05 (tol = 5.000e-09) r (rel) = 7.618e-07 (tol = 5.000e-09)\n", " Newton iteration 3: r (abs) = 1.035e-08 (tol = 5.000e-09) r (rel) = 1.216e-10 (tol = 5.000e-09)\n", " Newton solver finished in 3 iterations and 3 linear solver iterations.\n" ] } ], "source": [ "solver.parameters['newton_solver']['linear_solver'] = 'mumps'\n", "solver.parameters['newton_solver']['absolute_tolerance'] = 5e-9\n", "solver.parameters['newton_solver']['relative_tolerance'] = 5e-9\n", "\n", "ic = df.Expression((\"0.0\",\"0.0\",\"1.0\",\"0.0\",\"1.0\",\"0.0\"), degree = 1)\n", "w.assign(df.interpolate(ic, W))\n", "\n", "tick0 = time()\n", "solver.solve()\n", "tick1 = time()\n", "print(\"Elapsed time = \", tick1 - tick0)" ] }, { "cell_type": "markdown", "id": "95b4d2ce", "metadata": {}, "source": [ "Show results with pyplot." ] }, { "cell_type": "code", "execution_count": 9, "id": "8390e1fc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Plot of v[0] \n", "\n", "Object cannot be plotted directly, projecting to piecewise linears.\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Plot of v[1] \n", "\n", "Object cannot be plotted directly, projecting to piecewise linears.\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Plot of p \n", "\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Plot of Bxx \n", "\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Plot of Bxy \n", "\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Plot of Byy \n", "\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "(v, b11, b12, b22, p) = w.split() \n", "v.rename(\"v\", \"velocity\")\n", "p.rename(\"p\", \"pressure\")\n", "b11.rename(\"Bxx\", \"stress Bxx\")\n", "b12.rename(\"Bxy\", \"stress Bxy\")\n", "b22.rename(\"Byy\", \"stress Byy\")\n", "\n", "for unknown in v[0], v[1], p, b11, b12, b22:\n", " print(\"Plot of\", unknown, \"\\n\")\n", " figure = df.plot(unknown, cmap=plt.cm.hsv)\n", " plt.colorbar(figure)\n", " plt.show()" ] }, { "cell_type": "markdown", "id": "f1c7b081", "metadata": {}, "source": [ "Compare the numerical solution to the analytical solution." ] }, { "cell_type": "code", "execution_count": 10, "id": "178a26ba", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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", 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", 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", 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", 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X = np.linspace(R1, R2)\n", "\n", "V_num = [v(x, 0)[1] for x in X]\n", "V_anal = [(2.0/3.0)*(x - 1.0/x) for x in X]\n", "plt.plot(X, V_num, label='Numerical')\n", "plt.scatter(X, V_anal, label='Analytical', color='orange')\n", "plt.legend()\n", "plt.title('Velocity')\n", "plt.show()\n", "\n", "p_num = [p(x, 0) for x in X]\n", "p_anal = [(4.0/9.0)*((x**2)/2.0 - 2.0*np.log(x) - 1.0/(2.0*(x**2))) + (8.0/9.0)*(1.0/(x**4) - 1.0) for x in X]\n", "plt.plot(X, p_num, label='Numerical')\n", "plt.scatter(X, p_anal, label='Analytical', color='orange')\n", "plt.legend()\n", "plt.title('Pressure')\n", "plt.show()\n", "\n", "b11_num = [b11(x, 0) for x in X]\n", "b11_anal = [1.0 for x in X]\n", "plt.plot(X, b11_num, label='Numerical')\n", "plt.scatter(X, b11_anal, label='Analytical', color='orange')\n", "plt.legend()\n", "plt.title('Extra stress $B_{11}$')\n", "plt.show()\n", "\n", "b12_num = [b12(x, 0) for x in X]\n", "b12_anal = [4.0/(3.0*(x**2)) for x in X]\n", "plt.plot(X, b12_num, label='Numerical')\n", "plt.scatter(X, b12_anal, label='Analytical', color='orange')\n", "plt.legend()\n", "plt.title('Extra stress $B_{12}$')\n", "plt.show()\n", "\n", "b22_num = [b22(x, 0) for x in X]\n", "b22_anal = [1.0 + 32.0/(9.0*(x**4)) for x in X]\n", "plt.plot(X, b22_num, label='Numerical')\n", "plt.scatter(X, b22_anal, label='Analytical', color='orange')\n", "plt.legend()\n", "plt.title('Extra stress $B_{22}$')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "86fa36c5", "metadata": {}, "source": [ "## Exercises \n", "1) Modify the problem using the Navier-Stokes equations. How does the velocity field change?\n", "2) Experiment with different material parameters, make the spring stiffer, check the ratio $G/\\mu_1$.\n", "3) Experiment with different angular velocities.\n", "4) Try different mixed elements, c.f. to lecture on Poiseuille flow with the Stokes.\n", "5) Derive the analytical solution in polar coordinates." ] }, { "cell_type": "markdown", "id": "16da85b2", "metadata": {}, "source": [ "## Complete code" ] }, { "cell_type": "code", "execution_count": null, "id": "de35bd06", "metadata": {}, "outputs": [], "source": [ "import dolfin as df\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import mshr\n", "from time import time\n", "\n", "R1 = 1.0 # Radius R1\n", "R2 = 2.0 # Radius R2\n", "geometry = mshr.Circle(df.Point(0.0, 0.0), R2, 720) - mshr.Circle(df.Point(0.0, 0.0), R1, 720)\n", "\n", "mesh = mshr.generate_mesh(geometry, 70)\n", "mesh.init() \n", "df.plot(mesh)\n", "plt.show()\n", "\n", "# define boundary as a class\n", "class Inner(df.SubDomain):\n", " def inside(self, x, on_boundary):\n", " return on_boundary and x[0]*x[0]+x[1]*x[1]R2*R2-1.0e-3\n", "\n", "outer = Outer()\n", "\n", "# mark boundary parts\n", "bndry = df.MeshFunction('size_t', mesh, mesh.topology().dim()-1, 0)\n", "inner.mark(bndry, 1)\n", "outer.mark(bndry, 2)\n", "\n", "Ev = df.VectorElement(\"CG\", mesh.ufl_cell(), 2) # 2 = quadratic elements\n", "Ep = df.FiniteElement(\"CG\", mesh.ufl_cell(), 1) # 1 = linear elements\n", "E = df.MixedElement([Ev, Ep, Ep, Ep, Ep])\n", "W = df.FunctionSpace(mesh, E)\n", "print(\"Problem size: {0:d}\".format(W.dim())) \n", "\n", "outervel = df.Expression((\"-Omega*x[1]\", \"Omega*x[0]\"), Omega=0.5, degree=1)\n", "innervel = df.Expression((\"-Omega*x[1]\", \"Omega*x[0]\"), Omega=0.0, degree=1)\n", "\n", "bc_inner = df.DirichletBC(W.sub(0), innervel, bndry, 1) #inner radius\n", "bc_outer = df.DirichletBC(W.sub(0), outervel, bndry, 2) #outer radius\n", "bcp = df.DirichletBC(W.sub(4), df.Constant(0.0), \"near(x[0],1.0) && near(x[1],0.0)\", method=\"pointwise\") #Fix the pressure at one point\n", "\n", "bcs = [bc_outer, bc_inner, bcp] \n", "\n", "rho = df.Constant(1.0)\n", "mu1 = df.Constant(1.0)\n", "mu2 = df.Constant(1.0)\n", "G = df.Constant(1.0)\n", "\n", "v_, b11_, b12_, b22_, p_ = df.TestFunctions(W)\n", "w = df.Function(W)\n", "v, b11, b12, b22, p = df.split(w)\n", "\n", "B_ = df.as_tensor([[b11_,b12_],[b12_,b22_]])\n", "B = df.as_tensor([[b11,b12],[b12,b22]])\n", "\n", "I = df.Identity(mesh.geometry().dim())\n", "L = df.grad(v)\n", "D = 0.5*(L + L.T)\n", "matderv = df.grad(v)*v\n", "T = -p*I + 2.0*mu2*D + G*(B-I)\n", "oldroydderB = B.dx(0)*v[0] + B.dx(1)*v[1] - L*B - B*(L.T)\n", "\n", "Eq1 = df.div(v)*p_*df.dx\n", "Eq2 = df.inner(rho*matderv, v_)*df.dx + df.inner(T, df.grad(v_))*df.dx\n", "Eq3 = df.inner(oldroydderB, B_)*df.dx + mu1/G*df.inner(B - I, B_)*df.dx\n", "\n", "Eq = Eq1 + Eq2 + Eq3 \n", "\n", "problem=df.NonlinearVariationalProblem(Eq,w,bcs,df.derivative(Eq,w))\n", "solver=df.NonlinearVariationalSolver(problem)\n", "\n", "solver.parameters['newton_solver']['linear_solver'] = 'mumps'\n", "solver.parameters['newton_solver']['absolute_tolerance'] = 5e-9\n", "solver.parameters['newton_solver']['relative_tolerance'] = 5e-9\n", "\n", "ic = df.Expression((\"0.0\",\"0.0\",\"1.0\",\"0.0\",\"1.0\",\"0.0\"), degree = 1)\n", "w.assign(df.interpolate(ic, W))\n", "\n", "tick0 = time()\n", "solver.solve()\n", "tick1 = time()\n", "print(\"Elapsed time = \", tick1 - tick0)\n", "\n", "(v, b11, b12, b22, p) = w.split() \n", "v.rename(\"v\", \"velocity\")\n", "p.rename(\"p\", \"pressure\")\n", "b11.rename(\"Bxx\", \"stress Bxx\")\n", "b12.rename(\"Bxy\", \"stress Bxy\")\n", "b22.rename(\"Byy\", \"stress Byy\")\n", "\n", "for unknown in v[0], v[1], p, b11, b12, b22:\n", " print(\"Plot of\", unknown, \"\\n\")\n", " figure = df.plot(unknown, cmap=plt.cm.hsv)\n", " plt.colorbar(figure, location='bottom')\n", " plt.show()\n", "\t\n", "X = np.linspace(R1, R2)\n", "\n", "V_num = [v(x, 0)[1] for x in X]\n", "V_anal = [(2.0/3.0)*(x - 1.0/x) for x in X]\n", "plt.plot(X, V_num, label='Numerical')\n", "plt.scatter(X, V_anal, label='Analytical', color='orange')\n", "plt.legend()\n", "plt.title('Velocity')\n", "plt.show()\n", "\n", "p_num = [p(x, 0) for x in X]\n", "p_anal = [(4.0/9.0)*((x**2)/2.0 - 2.0*np.log(x) - 1.0/(2.0*(x**2))) + (8.0/9.0)*(1.0/(x**4) - 1.0) for x in X]\n", "plt.plot(X, p_num, label='Numerical')\n", "plt.scatter(X, p_anal, label='Analytical', color='orange')\n", "plt.legend()\n", "plt.title('Pressure')\n", "plt.show()\n", "\n", "b11_num = [b11(x, 0) for x in X]\n", "b11_anal = [1.0 for x in X]\n", "plt.plot(X, b11_num, label='Numerical')\n", "plt.scatter(X, b11_anal, label='Analytical', color='orange')\n", "plt.legend()\n", "plt.title('Extra stress $B_{11}$')\n", "plt.show()\n", "\n", "b12_num = [b12(x, 0) for x in X]\n", "b12_anal = [4.0/(3.0*(x**2)) for x in X]\n", "plt.plot(X, b12_num, label='Numerical')\n", "plt.scatter(X, b12_anal, label='Analytical', color='orange')\n", "plt.legend()\n", "plt.title('Extra stress $B_{12}$')\n", "plt.show()\n", "\n", "b22_num = [b22(x, 0) for x in X]\n", "b22_anal = [1.0 + 32.0/(9.0*(x**4)) for x in X]\n", "plt.plot(X, b22_num, label='Numerical')\n", "plt.scatter(X, b22_anal, label='Analytical', color='orange')\n", "plt.legend()\n", "plt.title('Extra stress $B_{22}$')\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.4" }, "vscode": { "interpreter": { "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1" } } }, "nbformat": 4, "nbformat_minor": 5 }