{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "During the Christmas holidays, I spent some time to convert my Matlab [FVTool](https://github.com/simulkade/FVTool) to a [Julia package](http://pkg.julialang.org/). The result, which I call [JFVM](https://github.com/simulkade/JFVM.jl) is a bit Matlabesque, but the package works. In this post I'm going to show how it works.\n", "\n", "## Installation\n", "To install the package, you can use \n", "```\n", "]add https://github.com/simulkade/JFVM.jl\n", "``` \n", "in Julia. You need to have Julia installed, of course! \n", "`JFVM` visualisation relies on `PyPlot` and `PyCall`. The visualization package can be installed by\n", "```\n", "]add https://github.com/simulkade/JFVMvis.jl\n", "``` \n", "\n", "## What does it do?\n", "It solves a transient convection-diffusion equation, i.e., $$\\alpha\\frac{\\partial\\phi}{\\partial t}+\\nabla.\\left(\\mathbf{u}\\phi\\right)+\\nabla.\\left(-D\\nabla\\phi\\right)+\\beta\\phi=\\gamma$$ with the boundary condition: $$a\\nabla\\phi.\\mathbf{e}+b\\phi=c.$$ Each term, i.e., transient, convection, diffusion, linear source, and constant source terms can be called via a separate function, which makes it possible to use the code for solving various coupled and even non-linear convection-diffusion equations. The main difference between this code and the previous Matlab version is that in this one, nonuniform grids can be defined. The supported coordinates are \n", " - 1D axisymmetric (radial)\n", " - 2D radial (r, theta)\n", " - 2D Cartesian\n", " - 3D Cartesian\n", " - 2D axisymmetric (cylindrical, r, z)\n", " - 3D cylindrical (r, theta, z)\n", "One other thing that I always had in mind is the possibility to use hetrogeneous transfer coefficients, e.g., a diffusion coefficient that is different on each cell. In addition, I wanted to be able to define different boundary conditions on the faces of the boundary cell. The last feature that I constantly miss in other PDE solvers is the Robin boundary condition, which can be defined quite easily in JFVM. \n", "One last feature that I added in later stages was the periodic boundary condition.\n", "\n", "## A simple example\n", "This is perhaps the simplest example: a diffusion equation on a 1D domain, with a Dirichlet boundary on each side. The equation read $$\\nabla (-D \\nabla \\phi) = 0$$ where $\\phi$ is zero on the left and one on the right side of the domain. The formulation in `JFVM` always follows this sequence:\n", " - Create a domain and mesh\n", " - Create a boundary for the domain (default: Neumann)\n", " - Change the boundary condition (optional)\n", " - Define the initial condition (optional, only if you have transient terms)\n", " - Define the transfer coefficients\n", " - Calculate the matrix of coefficients and RHS vector for each transfer term in the PDE\n", " - Call the linear solver\n", " - Call the visualization tool\n", "There can be other steps in between depending on the problems." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "using JFVM, JFVMvis, PyPlot" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject Text(37.0, 0.5, '$\\\\phi$')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L= 1.0 # length of the domain\n", "Nx= 20 # number of cells\n", "m= createMesh1D(Nx, L) # create the domain and mesh\n", "BC= createBC(m) # create the boundary condition\n", "BC.left.a .= 0.0 # left side Neumann term equal to zero\n", "BC.left.b .= 1.0 # left side Dirichlet term coefficient equal to one\n", "BC.left.c .= 0.0 # left side Dirichlet term value equal to zero\n", "BC.right.a .= 0.0\n", "BC.right.b .= 1.0\n", "BC.right.c .= 1.0\n", "D_val= 1.0 # value of the transfer coefficient\n", "D= createCellVariable(m, D_val) # assign D_val to all the cells\n", "# harmonic average of the transfer coefficient on the cell faces:\n", "D_face= harmonicMean(D)\n", "(Mbc, RHSbc)= boundaryConditionTerm(BC)\n", "Mdiff= diffusionTerm(D_face)\n", "M= Mdiff+Mbc # matrix of coefficients\n", "RHS= RHSbc # off course!\n", "phi= solveLinearPDE(m, M, RHS) # solve the linear PDE\n", "figure(figsize=(6.0,5.0)) # unit is [cm] for me\n", "visualizeCells(phi) # visualize the results\n", "# decorate the plot\n", "xlabel(\"x\", fontsize=16)\n", "ylabel(L\"\\phi\", fontsize=16)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A colorful a bit playful case\n", "The other night, my daughter wanted to see what I do with my computer. So I decided to solve an equation with fancy colorful results. So I created a diffusion process on a radial coordinate, Dirichlet boundary condition near the center of the circle (with alternationg zero-one values on the left boundary). I reduced the value of the diffusion coefficient in the direction of increasing $\\theta$ to increase the contrast in the result. Let me recreate it here." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "sys:1: MatplotlibDeprecationWarning: shading='flat' when X and Y have the same dimensions as C is deprecated since 3.3. Either specify the corners of the quadrilaterals with X and Y, or pass shading='auto', 'nearest' or 'gouraud', or set rcParams['pcolor.shading']. This will become an error two minor releases later.\n" ] }, { "data": { "text/plain": [ "PyObject " ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L= 1.0 # length of the domain\n", "Nx= 30 # number of cells\n", "Ntheta= 5*20\n", "m= createMeshRadial2D(Nx, Ntheta, L, 2π) # create the domain and mesh\n", "m.cellcenters.x .+= 0.1\n", "m.facecenters.x .+= 0.1\n", "BC= createBC(m) # create the boundary condition\n", "BC.left.a .= 0.0 # left side Neumann term equal to zero\n", "BC.left.b .= 1.0 # left side Dirichlet term coefficient equal to one\n", "BC.left.c .= 0.0 # left side Dirichlet term value equal to zero\n", "BC.left.c[1:5:Ntheta] .= 1.0\n", "BC.right.a .= 0.0\n", "BC.right.b .= 1.0\n", "BC.right.c .= 0.0\n", "BC.bottom.periodic=true # periodic boundary condition\n", "D_val= 1.0 # value of the transfer coefficient\n", "D= createCellVariable(m, D_val) # assign D_val to all the cells\n", "# harmonic average of the transfer coefficient on the cell faces:\n", "D_face= harmonicMean(D)\n", "D_face.yvalue .= 0.003*D_val\n", "(Mbc, RHSbc)= boundaryConditionTerm(BC)\n", "Mdiff= diffusionTerm(D_face)\n", "M= -Mdiff+Mbc # matrix of coefficients\n", "RHS= RHSbc # off course!\n", "phi= solveLinearPDE(m, M, RHS) # solve the linear PDE\n", "visualizeCells(phi) # visualize the results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Not really bad!\n", "That's it for now. I will come back with more real life examples." ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "kernelspec": { "display_name": "Julia 1.6.0", "language": "julia", "name": "julia-1.6" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.6.0" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }