{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "There are many cases where the transfer coefficient in the convection-diffusion equations is a function of the independent variable. This makes the PDE nonlinear. While working on my thesis, I realized that it is not that difficult to use the Taylor expansion to linearize the nonlinear terms in a PDE. Here, I'm going to give a simple example. In another post, I will explain how the same idea can be used to numerically solve the Buckley-Leverett equation.\n", "\n", "## The PDE\n", "I'm going to try a simple one here. I say try because I'm actually making it up right now. The equation reads $$\\frac{\\partial\\phi}{\\partial t}+\\nabla . (-D\\nabla \\phi) =0$$ where $$D=D_0(1+\\phi^2).$$ It means that the diffusion coefficient is increased when the concentration of the solute increases. \n", "To linearize this equation, I assume that $\\phi$ and $\\nabla \\phi$ are independent variables. Using Taylor expansion around a point $\\phi_0$, we can obtain the following general form: $$f\\left(\\phi\\right)\\nabla \\phi=f\\left(\\phi_{0}\\right)\\nabla \\phi+\\nabla \\phi_{0}\\left(\\frac{\\partial f}{\\partial \\phi}\\right)_{\\phi_{0}}\\left(\\phi-\\phi_{0}\\right).$$ In our case, this equation simplifies to $$D_0(1+\\phi^2)\\nabla \\phi=D_0(1+\\phi_0^2)\\nabla \\phi+2D_0\\phi_0\\nabla \\phi_0(\\phi-\\phi_0).$$ Putting back everythin together, we obtain this linearized form for our PDE $$\\frac{\\partial\\phi}{\\partial t}+\\nabla.(-D_{0}(1+\\phi_{0}^{2})\\nabla\\phi)+\\nabla.(-2D_{0}\\phi_{0}\\nabla\\phi_{0}\\phi)=\\nabla.(-2D_{0}\\phi_{0}\\nabla\\phi_{0}\\phi_{0}).$$ Don't freak out! This equation is actually quite simple. By linearizing, we have added a linear convection term to our nonlinear diffusion equation. This equation is still an approximation of the real PDE. We have to solve the linear equation for $\\phi$ by initializing $\\phi_0$. Then, we assign the new value of $\\phi$ to $\\phi_0$ until it converges to a solution. The question that still remains is that \"is this really a good idea to make a diffusion equation more complicated by adding a convection term to it?\". \n", "\n", "\n", "\n", "\n", "\n", "## The solution procedure\n", "Solving this equation is done in two loops. The outer loop is for the time steps, and the inner loop is for the nonlinear equation. We will assemple an equation which looks like this: $$\\text{Transient}(\\Delta t,\\phi)-\\text{Diffusion}(D(\\phi_0),\\phi)+\\text{Convection}(\\mathbf{u}(\\phi_0),\\phi)=\\text{divergence}(D(\\phi_0), \\nabla\\phi_0)$$\n", "\n", "## Implementation in JFVM\n", "Here, I'll implement the procedure in [JFVM](http://github.com/simulkade/JFVM.jl). The same procedure can be done in [FVtool](http://github.com/simulkade/FVTool)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO: Loading help data...\n" ] } ], "source": [ "using JFVM, PyPlot" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "diffusion_newton (generic function with 1 method)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function diffusion_newton()\n", "L= 1.0 # domain length\n", "Nx= 100 # number of cells\n", "m= createMesh1D(Nx, L) # create a 1D mesh\n", "D0= 1.0 # diffusion coefficient constant\n", "# Define the diffusion coefficientand its derivative\n", "D(phi)=D0*(1.0+phi.^2)\n", "dD(phi)=2.0*D0*phi\n", "# create boundary condition\n", "BC = createBC(m)\n", "BC.left.a[:]=0.0\n", "BC.left.b[:]=1.0\n", "BC.left.c[:]=5.0\n", "BC.right.a[:]=0.0\n", "BC.right.b[:]=1.0\n", "BC.right.c[:]=0.0\n", "(Mbc, RHSbc)= boundaryConditionTerm(BC)\n", "# define the initial condition\n", "phi0= 0.0 # initial value\n", "phi_old= createCellVariable(m, phi0, BC) # create initial cells\n", "phi_val= copyCell(phi_old)\n", "# define the time steps\n", "dt= 0.001*L*L/D0 # a proper time step for diffusion process\n", "for i=1:10\n", " err=100\n", " (Mt, RHSt) = transientTerm(phi_old, dt)\n", " while err>1e-10\n", " # calculate the diffusion coefficient\n", " Dface= harmonicMean(cellEval(D,phi_val))\n", " # calculate the face value of phi_0\n", " phi_face= linearMean(phi_val)\n", " # calculate the velocity for convection term\n", " u= faceEval(dD, phi_face).*gradientTerm(phi_val)\n", " # diffusion term\n", " Mdif= diffusionTerm(Dface)\n", " # convection term\n", " Mconv= convectionTerm(u)\n", " # divergence term on the RHS\n", " RHSlin= divergenceTerm(u.*phi_face)\n", " # matrix of coefficients\n", " M= Mt-Mdif-Mconv+Mbc\n", " # RHS vector\n", " RHS= RHSbc+RHSt-RHSlin\n", " # call the linear solver\n", " phi_new= solveLinearPDE(m, M, RHS)\n", " # calculate the error\n", " err= maximum(abs(phi_new.value-phi_val.value))\n", " # assign the new phi to the old phi\n", " phi_val=copyCell(phi_new)\n", " end\n", " phi_old= copyCell(phi_val)\n", " visualizeCells(phi_val)\n", "end\n", " return phi_val\n", "end" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "elapsed time: 0.065438686 seconds (15208324 bytes allocated)\n" ] }, { "data": { "image/png": [ 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" 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"source": [ "The solution looks quite good. The diffusion coefficient is higher at higher concentrations, and it can be clearly observed in the above concentration profile (if you compare it with a diffusion problem with constant diffusion coefficient, in your head).\n", "## Some questions\n", "The convection term that appears after linearization of the problem has a velocity term, which reads $$\\mathbf{u}(\\phi_0)=−2.0D_0\\phi_0\\nabla\\phi_0$$ I have written a function, called `gradientTerm` which gives you the value of the gradient on the cell faces. This gradient is multiplied by a term that needs to be averaged on each cell face. Here, I have calculated the arithmetic average of $\\phi_0$ using a function called suprise suprise `linearMean`. This is of course one way of doing it. The other ways are `geometricMean`, `harmonicMean`, `upwindMean`, `tvdMean`, and `aritheticMean`. Here, we will discuss them.\n", "## Averaging techniques for the face values in FVM\n", "The following figure shows two neigbor cells with different length and values. \n", "![neighbor cells FVM](/averaging_pic.png)\n", "The averaging terms that are used in JFVM are as follows:\n", "### Linear mean\n", "It is equivalent to a linear interpolation or the lever rule. It reads $$\\phi_{face}=\\frac{\\Delta x_1\\phi_2+\\Delta x_2\\phi_1}{\\Delta x_1+\\Delta x_2}$$\n", "### Arithmetic mean\n", "The value of each cell is weighted by its length: $$\\phi_{face}=\\frac{\\Delta x_1\\phi_1+\\Delta x_2\\phi_2}{\\Delta x_1+\\Delta x_2}$$\n", "### Geometric mean\n", "It reads $$\\phi_{face}=\\exp\\left(\\frac{\\Delta x_1\\log(\\phi_1)+\\Delta x_2\\log(\\phi_2)}{\\Delta x_1+\\Delta x_2}\\right)$$\n", "### Harmonic mean\n", "It reads $$\\phi_{face}=\\frac{\\Delta x_1+\\Delta x_2}{\\Delta x_1/\\phi_1+\\Delta x_2/\\phi_2}$$\n", "Note that if the value of one of the cells is zero, the geometric and harmonic means are also equal to zero. \n", "These methods have different applications for different ptoblems. We will discuss them in future posts.\n", "## Direct substitution\n", "The diffusion problem that we solved above can also be solved using a direct substitution method. Here, we don't use the derivatives and no linearization is required. The code is written here:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "diffusion_direct (generic function with 1 method)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function diffusion_direct()\n", "L= 1.0 # domain length\n", "Nx= 100 # number of cells\n", "m= createMesh1D(Nx, L) # create a 1D mesh\n", "D0= 1.0 # diffusion coefficient constant\n", "# Define the diffusion coefficientand its derivative\n", "D(phi)=D0*(1.0+phi.^2)\n", "dD(phi)=2.0*D0*phi\n", "# create boundary condition\n", "BC = createBC(m)\n", "BC.left.a[:]=0.0\n", "BC.left.b[:]=1.0\n", "BC.left.c[:]=5.0\n", "BC.right.a[:]=0.0\n", "BC.right.b[:]=1.0\n", "BC.right.c[:]=0.0\n", "(Mbc, RHSbc)= boundaryConditionTerm(BC)\n", "# define the initial condition\n", "phi0= 0.0 # initial value\n", "phi_old= createCellVariable(m, phi0, BC) # create initial cells\n", "phi_val= copyCell(phi_old)\n", "# define the time steps\n", "dt= 0.001*L*L/D0 # a proper time step for diffusion process\n", "for i=1:10\n", " err=100\n", " (Mt, RHSt) = transientTerm(phi_old, dt)\n", " while err>1e-10\n", " # calculate the diffusion coefficient\n", " Dface= harmonicMean(cellEval(D,phi_val))\n", " # diffusion term\n", " Mdif= diffusionTerm(Dface)\n", " # matrix of coefficients\n", " M= Mt-Mdif+Mbc\n", " # RHS vector\n", " RHS= RHSbc+RHSt\n", " # call the linear solver\n", " phi_new= solveLinearPDE(m, M, RHS)\n", " # calculate the error\n", " err= maximum(abs(phi_new.value-phi_val.value))\n", " # assign the new phi to the old phi\n", " phi_val=copyCell(phi_new)\n", " end\n", " phi_old= copyCell(phi_val)\n", " visualizeCells(phi_val)\n", "end\n", " return phi_val\n", "end" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "elapsed time: 0.115909663 seconds (22458788 bytes allocated, 26.14% gc time)\n" ] }, { "data": { "image/png": [ 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" ], "text/plain": [ "Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "CellValue{Float64}(MeshStructure(1,[100],CellSize{Float64}([0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01 … 0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01],[0.0],[0.0]),CellLocation{Float64}([0.005,0.015,0.025,0.035,0.045,0.055,0.065,0.075,0.085,0.095 … 0.905,0.915,0.925,0.935,0.945,0.955,0.965,0.975,0.985,0.995],[0.0],[0.0]),FaceLocation{Float64}([0.0,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09 … 0.91,0.92,0.93,0.94,0.95,0.96,0.97,0.98,0.99,1.0],[0.0],[0.0]),[1],[1]),[5.0196,4.9804,4.94059,4.90018,4.85914,4.81745,4.77511,4.7321,4.68839,4.64398 … 0.000323843,0.000250452,0.000192389,0.000146146,0.000108911,7.84098e-5,5.27679e-5,3.04028e-5,9.92833e-6,-9.92833e-6])" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@time phi_ds=diffusion_direct()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Show and compare the results\n", "Here, I'm plotting the results of the Newton and the direct substitution methods for comparison." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ 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" ], "text/plain": [ "Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject " ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(phi_ds.domain.cellcenters.x, phi_ds.value[2:end-1], \"y\",\n", "phi_n.domain.cellcenters.x, phi_n.value[2:end-1], \"--r\") \n", "legend([\"direct subs\", \"Newton\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "The final results shows that we can linearize a nonlinear PDE, relatively easily and solve the equations using a linear PDE solver. No difference is observed between the final results of the direct substitution method (with no linearization) and the Newton method (with a linearized PDE). We can also observe that, as expected, the Newton method is relatively faster." ] } ], "metadata": { "kernelspec": { "display_name": "Julia 0.3.6", "language": "julia", "name": "julia 0.3" }, "language_info": { "name": "julia", "version": "0.3.7" } }, "nbformat": 4, "nbformat_minor": 0 }