265 lines
7.1 KiB
C++
265 lines
7.1 KiB
C++
// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
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// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
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// LICENSE and NOTICE for details. LLNL-CODE-806117.
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//
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// This file is part of the MFEM library. For more information and source code
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// availability visit https://mfem.org.
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//
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// MFEM is free software; you can redistribute it and/or modify it under the
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// terms of the BSD-3 license. We welcome feedback and contributions, see file
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// CONTRIBUTING.md for details.
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//
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// Navier Kovasznay example
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//
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// Solve for the steady Kovasznay flow at Re = 40 defined by
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//
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// u = [1 - exp(L * x) * cos(2 * pi * y),
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// L / (2 * pi) * exp(L * x) * sin(2 * pi * y)],
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//
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// p = 1/2 * (1 - exp(2 * L * x)),
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//
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// with L = Re/2 - sqrt(Re^2/4 + 4 * pi^2).
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//
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// The problem domain is set up like this
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//
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// +-------------+
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// | |
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// | |
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// | |
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// | |
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// Inflow -> | | -> Outflow
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// | |
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// | |
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// | |
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// | |
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// | |
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// +-------------+
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//
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// and Dirichlet boundary conditions are applied for the velocity on every
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// boundary. The problem, although steady state, is time integrated up to the
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// final time and the solution is compared with the known exact solution.
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#include "navier_solver.hpp"
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#include <fstream>
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using namespace mfem;
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using namespace navier;
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struct s_NavierContext
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{
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int ser_ref_levels = 1;
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int order = 6;
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double kinvis = 1.0 / 40.0;
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double t_final = 10 * 0.001;
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double dt = 0.001;
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double reference_pressure = 0.0;
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double reynolds = 1.0 / kinvis;
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double lam = 0.5 * reynolds
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- sqrt(0.25 * reynolds * reynolds + 4.0 * M_PI * M_PI);
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bool pa = true;
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bool ni = false;
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bool visualization = false;
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bool checkres = false;
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} ctx;
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void vel_kovasznay(const Vector &x, double t, Vector &u)
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{
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double xi = x(0);
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double yi = x(1);
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u(0) = 1.0 - exp(ctx.lam * xi) * cos(2.0 * M_PI * yi);
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u(1) = ctx.lam / (2.0 * M_PI) * exp(ctx.lam * xi) * sin(2.0 * M_PI * yi);
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}
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double pres_kovasznay(const Vector &x, double t)
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{
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double xi = x(0);
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return 0.5 * (1.0 - exp(2.0 * ctx.lam * xi)) + ctx.reference_pressure;
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}
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int main(int argc, char *argv[])
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{
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MPI_Session mpi(argc, argv);
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OptionsParser args(argc, argv);
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args.AddOption(&ctx.ser_ref_levels,
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"-rs",
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"--refine-serial",
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"Number of times to refine the mesh uniformly in serial.");
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args.AddOption(&ctx.order,
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"-o",
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"--order",
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"Order (degree) of the finite elements.");
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args.AddOption(&ctx.dt, "-dt", "--time-step", "Time step.");
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args.AddOption(&ctx.t_final, "-tf", "--final-time", "Final time.");
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args.AddOption(&ctx.pa,
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"-pa",
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"--enable-pa",
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"-no-pa",
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"--disable-pa",
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"Enable partial assembly.");
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args.AddOption(&ctx.ni,
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"-ni",
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"--enable-ni",
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"-no-ni",
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"--disable-ni",
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"Enable numerical integration rules.");
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args.AddOption(&ctx.visualization,
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"-vis",
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"--visualization",
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"-no-vis",
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"--no-visualization",
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"Enable or disable GLVis visualization.");
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args.AddOption(
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&ctx.checkres,
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"-cr",
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"--checkresult",
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"-no-cr",
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"--no-checkresult",
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"Enable or disable checking of the result. Returns -1 on failure.");
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args.Parse();
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if (!args.Good())
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{
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if (mpi.Root())
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{
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args.PrintUsage(mfem::out);
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}
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return 1;
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}
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if (mpi.Root())
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{
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args.PrintOptions(mfem::out);
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}
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Mesh *mesh = new Mesh(2, 4, Element::QUADRILATERAL, false, 1.5, 2.0);
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mesh->EnsureNodes();
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GridFunction *nodes = mesh->GetNodes();
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*nodes -= 0.5;
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for (int i = 0; i < ctx.ser_ref_levels; ++i)
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{
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mesh->UniformRefinement();
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}
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if (mpi.Root())
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{
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std::cout << "Number of elements: " << mesh->GetNE() << std::endl;
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}
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auto *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
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delete mesh;
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// Create the flow solver.
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NavierSolver flowsolver(pmesh, ctx.order, ctx.kinvis);
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flowsolver.EnablePA(ctx.pa);
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flowsolver.EnableNI(ctx.ni);
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// Set the initial condition.
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ParGridFunction *u_ic = flowsolver.GetCurrentVelocity();
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VectorFunctionCoefficient u_excoeff(pmesh->Dimension(), vel_kovasznay);
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u_ic->ProjectCoefficient(u_excoeff);
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FunctionCoefficient p_excoeff(pres_kovasznay);
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// Add Dirichlet boundary conditions to velocity space restricted to
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// selected attributes on the mesh.
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Array<int> attr(pmesh->bdr_attributes.Max());
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attr = 1;
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flowsolver.AddVelDirichletBC(vel_kovasznay, attr);
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double t = 0.0;
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double dt = ctx.dt;
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double t_final = ctx.t_final;
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bool last_step = false;
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flowsolver.Setup(dt);
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double err_u = 0.0;
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double err_p = 0.0;
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ParGridFunction *u_gf = nullptr;
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ParGridFunction *p_gf = nullptr;
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ParGridFunction p_ex_gf(flowsolver.GetCurrentPressure()->ParFESpace());
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GridFunctionCoefficient p_ex_gf_coeff(&p_ex_gf);
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for (int step = 0; !last_step; ++step)
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{
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if (t + dt >= t_final - dt / 2)
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{
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last_step = true;
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}
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flowsolver.Step(t, dt, step);
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// Compare against exact solution of velocity and pressure.
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u_gf = flowsolver.GetCurrentVelocity();
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p_gf = flowsolver.GetCurrentPressure();
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u_excoeff.SetTime(t);
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p_excoeff.SetTime(t);
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// Remove mean value from exact pressure solution.
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p_ex_gf.ProjectCoefficient(p_excoeff);
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flowsolver.MeanZero(p_ex_gf);
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err_u = u_gf->ComputeL2Error(u_excoeff);
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err_p = p_gf->ComputeL2Error(p_ex_gf_coeff);
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double cfl = flowsolver.ComputeCFL(*u_gf, dt);
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if (mpi.Root())
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{
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printf("%5s %8s %8s %8s %11s %11s\n",
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"Order",
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"CFL",
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"Time",
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"dt",
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"err_u",
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"err_p");
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printf("%5.2d %8.2E %.2E %.2E %.5E %.5E err\n",
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ctx.order,
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cfl,
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t,
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dt,
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err_u,
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err_p);
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fflush(stdout);
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}
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}
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if (ctx.visualization)
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{
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char vishost[] = "localhost";
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int visport = 19916;
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socketstream sol_sock(vishost, visport);
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sol_sock.precision(8);
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sol_sock << "parallel " << mpi.WorldSize() << " " << mpi.WorldRank()
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<< "\n";
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sol_sock << "solution\n" << *pmesh << *u_ic << std::flush;
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}
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flowsolver.PrintTimingData();
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// Test if the result for the test run is as expected.
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if (ctx.checkres)
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{
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double tol_u = 1e-6;
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double tol_p = 1e-5;
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if (err_u > tol_u || err_p > tol_p)
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{
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if (mpi.Root())
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{
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mfem::out << "Result has a larger error than expected."
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<< std::endl;
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}
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return -1;
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}
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}
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delete pmesh;
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return 0;
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}
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