void verify(Config& orig) {
// FIXME: doesn't fully check result
checkHeights();
checkConservation(orig);
checkAugmentingPath();
}
int main(int argc, char *argv[])
{
// Process command line arguments
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr beta_n_u_hat = varFactory.fluxVar("\\widehat{\\beta \\cdot n }");
VarPtr u = varFactory.fieldVar("u");
FunctionPtr beta = Teuchos::rcp(new Beta());
//////////////////// BUILD MESH ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
meshBoundary(0,0) = -1.0; // x1
meshBoundary(0,1) = -1.0; // y1
meshBoundary(1,0) = 1.0;
meshBoundary(1,1) = -1.0;
meshBoundary(2,0) = 1.0;
meshBoundary(2,1) = 1.0;
meshBoundary(3,0) = -1.0;
meshBoundary(3,1) = 1.0;
int horizontalCells = 32, verticalCells = 32;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
confusionBF, H1Order, H1Order+pToAdd);
////////////////////////////////////////////////////////////////////
// INITIALIZE FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr prevTimeFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
SolutionPtr flowResidual = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
FunctionPtr u_prev_time = Teuchos::rcp( new PreviousSolutionFunction(prevTimeFlow, u) );
//////////////////// DEFINE BILINEAR FORM ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr invDt = Teuchos::rcp(new ScalarParamFunction(1.0/dt));
// v terms:
confusionBF->addTerm( beta * u, - v->grad() );
confusionBF->addTerm( beta_n_u_hat, v);
confusionBF->addTerm( u, invDt*v );
rhs->addTerm( u_prev_time * invDt * v );
//////////////////// SPECIFY RHS ///////////////////////
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr ip = confusionBF->graphNorm();
// IPPtr ip = Teuchos::rcp(new IP);
// ip->addTerm(v);
// ip->addTerm(invDt*v - beta*v->grad());
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary(beta) );
FunctionPtr u0 = Teuchos::rcp( new ConstantScalarFunction(0) );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
bc->addDirichlet(beta_n_u_hat, inflowBoundary, beta*n*u0);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(prevTimeFlow);
mesh->registerSolution(flowResidual);
// ==================== SET INITIAL GUESS ==========================
FunctionPtr u_init = Teuchos::rcp(new InitialCondition());
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u->ID()] = u_init;
prevTimeFlow->projectOntoMesh(functionMap);
//////////////////// SOLVE & REFINE ///////////////////////
// if (enforceLocalConservation) {
// // FunctionPtr parity = Teuchos::rcp<Function>( new SideParityFunction );
// // LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(parity, beta_n_u_minus_sigma_n) );
// LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(1.0, beta_n_u_minus_sigma_n) );
// LinearTermPtr sourcePart = Teuchos::rcp<LinearTerm>( new LinearTerm(invDt, u) );
// conservedQuantity->addTerm(sourcePart, true);
// solution->lagrangeConstraints()->addConstraint(conservedQuantity == u_prev_time * invDt);
// }
int timestepCount = 0;
double time_tol = 1e-8;
double L2_time_residual = 1e9;
while((L2_time_residual > time_tol) && (timestepCount < numTimeSteps))
{
solution->solve(false);
// Subtract solutions to get residual
flowResidual->setSolution(solution);
flowResidual->addSolution(prevTimeFlow, -1.0);
L2_time_residual = flowResidual->L2NormOfSolutionGlobal(u->ID());
if (rank == 0)
{
cout << endl << "Timestep: " << timestepCount << ", dt = " << dt << ", Time residual = " << L2_time_residual << endl;
stringstream outfile;
outfile << "rotatingCylinder_" << timestepCount;
solution->writeToVTK(outfile.str(), 5);
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
FunctionPtr source = Teuchos::rcp( new PreviousSolutionFunction(flowResidual, u) );
source = invDt * source;
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, source, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
prevTimeFlow->setSolution(solution); // reset previous time solution to current time sol
timestepCount++;
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
double epsilon = args.Input<double>("--epsilon", "diffusion parameter");
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = modified robust");
// Optional arguments (have defaults)
bool zeroL2 = args.Input("--zeroL2", "take L2 term on v in robust norm to zero", false);
args.Process();
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma = varFactory.fieldVar("sigma", VECTOR_L2);
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma / epsilon, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (norm == 0)
{
ip = bf->graphNorm();
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
ip->addZeroMeanTerm( h2_scaling*v );
}
// Robust norm
else if (norm == 1)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
// Weight these two terms for inflow
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
// Modified robust norm
else if (norm == 2)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
// FunctionPtr ip_weight = Teuchos::rcp( new IPWeight() );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() - beta*v->grad() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
// // robust test norm
// IPPtr robIP = Teuchos::rcp(new IP);
// FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
// if (!enforceLocalConservation)
// robIP->addTerm( ip_scaling * v );
// robIP->addTerm( sqrt(epsilon) * v->grad() );
// // Weight these two terms for inflow
// FunctionPtr ip_weight = Teuchos::rcp( new IPWeight() );
// robIP->addTerm( ip_weight * beta * v->grad() );
// robIP->addTerm( ip_weight * tau->div() );
// robIP->addTerm( ip_scaling/sqrt(epsilon) * tau );
// if (enforceLocalConservation)
// robIP->addZeroMeanTerm( v );
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
SpatialFilterPtr lBoundary = Teuchos::rcp( new LeftBoundary );
SpatialFilterPtr tbBoundary = Teuchos::rcp( new TopBottomBoundary );
SpatialFilterPtr rBoundary = Teuchos::rcp( new RightBoundary );
// SpatialFilterPtr leftCircleBoundary = Teuchos::rcp( new LeftCircleBoundary );
// SpatialFilterPtr rightCircleBoundary = Teuchos::rcp( new RightCircleBoundary );
SpatialFilterPtr circleBoundary = Teuchos::rcp( new CircleBoundary );
bc->addDirichlet(beta_n_u_minus_sigma_n, lBoundary, zero);
bc->addDirichlet(beta_n_u_minus_sigma_n, tbBoundary, zero);
pc->addConstraint(beta*uhat->times_normal() - beta_n_u_minus_sigma_n == zero, rBoundary);
// bc->addDirichlet(uhat, leftCircleBoundary, one);
// bc->addDirichlet(beta_n_u_minus_sigma_n, rightCircleBoundary, beta*n*one);
bc->addDirichlet(uhat, circleBoundary, one);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 3, pToAdd = 2;
Teuchos::RCP<Mesh> mesh;
mesh = MeshFactory::shiftedHemkerMesh(-3, 9, 6, 1, bf, H1Order, pToAdd);
// mesh = BuildHemkerMesh(bf, nseg, circleMesh, triangulateMesh, H1Order, pToAdd);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->setFilter(pc);
if (enforceLocalConservation)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
}
double energyThreshold = 0.25; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
Teuchos::RCP<RefinementHistory> refHistory = Teuchos::rcp( new RefinementHistory );
mesh->registerObserver(refHistory);
#ifdef saveVTK
VTKExporter exporter(solution, mesh, varFactory);
#endif
ofstream errOut;
if (commRank == 0)
errOut.open("hemker_err.txt");
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
solution->solve(false);
double energy_error = solution->energyErrorTotal();
if (commRank==0)
{
stringstream outfile;
outfile << "hemker_" << refIndex;
#ifdef saveVTK
exporter.exportSolution(outfile.str());
#endif
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_sigma_n) );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
errOut << mesh->numGlobalDofs() << " " << energy_error << " "
<< fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
if (commRank == 0)
errOut.close();
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = coupled robust");
// Optional arguments (have defaults)
int uniformRefinements = args.Input("--uniformRefinements", "number of uniform refinements", 0);
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation", false);
double radius = args.Input("--r", "cylinder radius", 0.6);
int Re = args.Input("--Re", "Reynolds number", 1);
int maxNewtonIterations = args.Input("--maxIterations", "maximum number of Newton iterations", 1);
int polyOrder = args.Input("--polyOrder", "polynomial order for field variables", 2);
int deltaP = args.Input("--deltaP", "how much to enrich test space", 2);
// string saveFile = args.Input<string>("--meshSaveFile", "file to which to save refinement history", "");
// string replayFile = args.Input<string>("--meshLoadFile", "file with refinement history to replay", "");
args.Process();
//////////////////// PROBLEM DEFINITIONS ///////////////////////
int H1Order = polyOrder+1;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau1 = varFactory.testVar("tau1", HDIV);
VarPtr tau2 = varFactory.testVar("tau2", HDIV);
VarPtr v1 = varFactory.testVar("v1", HGRAD);
VarPtr v2 = varFactory.testVar("v2", HGRAD);
VarPtr vc = varFactory.testVar("vc", HGRAD);
// define trial variables
VarPtr u1 = varFactory.fieldVar("u1");
VarPtr u2 = varFactory.fieldVar("u2");
VarPtr p = varFactory.fieldVar("p");
VarPtr u1hat = varFactory.traceVar("u1hat");
VarPtr u2hat = varFactory.traceVar("u2hat");
VarPtr t1hat = varFactory.fluxVar("t1hat");
VarPtr t2hat = varFactory.fluxVar("t2hat");
VarPtr sigma1 = varFactory.fieldVar("sigma1", VECTOR_L2);
VarPtr sigma2 = varFactory.fieldVar("sigma2", VECTOR_L2);
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshFactory::shiftedHemkerMesh(-1, 3, 2, radius, bf, H1Order, deltaP);
////////////////////////////////////////////////////////////////////
// INITIALIZE BACKGROUND FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
vector<double> e1(2); // (1,0)
e1[0] = 1;
vector<double> e2(2); // (0,1)
e2[1] = 1;
FunctionPtr u1_prev = Function::solution(u1, backgroundFlow);
FunctionPtr u2_prev = Function::solution(u2, backgroundFlow);
FunctionPtr sigma1_prev = Function::solution(sigma1, backgroundFlow);
FunctionPtr sigma2_prev = Function::solution(sigma2, backgroundFlow);
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
FunctionPtr beta = e1 * u1_prev + e2 * u2_prev;
// ==================== SET INITIAL GUESS ==========================
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u1->ID()] = one;
functionMap[u2->ID()] = zero;
functionMap[sigma1->ID()] = Function::vectorize(zero,zero);
functionMap[sigma2->ID()] = Function::vectorize(zero,zero);
functionMap[p->ID()] = zero;
backgroundFlow->projectOntoMesh(functionMap);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
// // stress equation
bf->addTerm( sigma1, tau1 );
bf->addTerm( sigma2, tau2 );
bf->addTerm( u1, tau1->div() );
bf->addTerm( u2, tau2->div() );
bf->addTerm( -u1hat, tau1->dot_normal() );
bf->addTerm( -u2hat, tau2->dot_normal() );
// momentum equation
// bf->addTerm( Function::xPart(sigma1_prev)*u1, v1 );
// bf->addTerm( Function::yPart(sigma1_prev)*u2, v1 );
// bf->addTerm( Function::xPart(sigma2_prev)*u1, v2 );
// bf->addTerm( Function::yPart(sigma2_prev)*u2, v2 );
// bf->addTerm( beta*sigma1, v1);
// bf->addTerm( beta*sigma2, v2);
bf->addTerm( 1./Re*sigma1, v1->grad() );
bf->addTerm( 1./Re*sigma2, v2->grad() );
bf->addTerm( t1hat, v1);
bf->addTerm( t2hat, v2);
bf->addTerm( -p, v1->dx() );
bf->addTerm( -p, v2->dy() );
// continuity equation
bf->addTerm( -u1, vc->dx() );
bf->addTerm( -u2, vc->dy() );
bf->addTerm( u1hat, vc->times_normal_x() );
bf->addTerm( u2hat, vc->times_normal_y() );
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
// stress equation
rhs->addTerm( -sigma1_prev * tau1 );
rhs->addTerm( -sigma2_prev * tau2 );
rhs->addTerm( -u1_prev * tau1->div() );
rhs->addTerm( -u2_prev * tau2->div() );
// momentum equation
// rhs->addTerm( -beta*sigma1_prev * v1 );
// rhs->addTerm( -beta*sigma2_prev * v2 );
rhs->addTerm( -1./Re*sigma1_prev * v1->grad() );
rhs->addTerm( -1./Re*sigma2_prev * v2->grad() );
// continuity equation
rhs->addTerm( u1_prev * vc->dx() );
rhs->addTerm( u2_prev * vc->dy() );
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (norm == 0)
{
ip = bf->graphNorm();
}
else if (norm == 1)
{
// ip = bf->l2Norm();
}
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr left = Teuchos::rcp( new ConstantXBoundary(-1) );
SpatialFilterPtr right = Teuchos::rcp( new ConstantXBoundary(3) );
SpatialFilterPtr top = Teuchos::rcp( new ConstantYBoundary(1) );
SpatialFilterPtr bottom = Teuchos::rcp( new ConstantYBoundary(-1) );
SpatialFilterPtr circle = Teuchos::rcp( new CircleBoundary(radius) );
FunctionPtr boundaryU1 = Teuchos::rcp( new BoundaryU1 );
bc->addDirichlet(u1hat, left, boundaryU1);
bc->addDirichlet(u2hat, left, zero);
bc->addDirichlet(u1hat, right, boundaryU1);
bc->addDirichlet(u2hat, right, zero);
bc->addDirichlet(u1hat, top, zero);
bc->addDirichlet(u2hat, top, zero);
bc->addDirichlet(u1hat, bottom, zero);
bc->addDirichlet(u2hat, bottom, zero);
bc->addDirichlet(u1hat, circle, zero);
bc->addDirichlet(u2hat, circle, zero);
// zero mean constraint on pressure
bc->addZeroMeanConstraint(p);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
if (enforceLocalConservation)
{
solution->lagrangeConstraints()->addConstraint(u1hat->times_normal_x() + u2hat->times_normal_y() == zero);
}
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(backgroundFlow);
// Teuchos::RCP< RefinementHistory > refHistory = Teuchos::rcp( new RefinementHistory );
// mesh->registerObserver(refHistory);
//////////////////// SOLVE & REFINE ///////////////////////
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(backgroundFlow, mesh, varFactory);
ofstream errOut;
ofstream fluxOut;
if (commRank == 0)
{
errOut.open("stokeshemker_err.txt");
fluxOut.open("stokeshemker_flux.txt");
}
errOut.precision(15);
fluxOut.precision(15);
// Cell IDs for flux calculations
vector< pair<ElementPtr, int> > cellFace0;
vector< pair<ElementPtr, int> > cellFace1;
vector< pair<ElementPtr, int> > cellFace2;
vector< pair<ElementPtr, int> > cellFace3;
vector< pair<ElementPtr, int> > cellFace4;
cellFace0.push_back(make_pair(mesh->getElement(12), 3));
cellFace0.push_back(make_pair(mesh->getElement(13), 3));
cellFace0.push_back(make_pair(mesh->getElement(14), 3));
cellFace0.push_back(make_pair(mesh->getElement(15), 3));
cellFace1.push_back(make_pair(mesh->getElement(12), 1));
cellFace1.push_back(make_pair(mesh->getElement(13), 1));
cellFace1.push_back(make_pair(mesh->getElement(14), 1));
cellFace1.push_back(make_pair(mesh->getElement(15), 1));
cellFace2.push_back(make_pair(mesh->getElement(11), 1));
cellFace2.push_back(make_pair(mesh->getElement(2 ), 0));
cellFace2.push_back(make_pair(mesh->getElement(5 ), 2));
cellFace2.push_back(make_pair(mesh->getElement(16), 1));
cellFace3.push_back(make_pair(mesh->getElement(9 ), 3));
cellFace3.push_back(make_pair(mesh->getElement(8 ), 3));
cellFace3.push_back(make_pair(mesh->getElement(19), 3));
cellFace3.push_back(make_pair(mesh->getElement(18), 3));
cellFace4.push_back(make_pair(mesh->getElement(9 ), 1));
cellFace4.push_back(make_pair(mesh->getElement(8 ), 1));
cellFace4.push_back(make_pair(mesh->getElement(19), 1));
cellFace4.push_back(make_pair(mesh->getElement(18), 1));
// // for loading refinement history
// if (replayFile.length() > 0) {
// RefinementHistory refHistory;
// replayFile = replayFile;
// refHistory.loadFromFile(replayFile);
// refHistory.playback(mesh);
// int numElems = mesh->numActiveElements();
// if (commRank==0){
// double minSideLength = meshInfo.getMinCellSideLength() ;
// cout << "after replay, num elems = " << numElems << " and min side length = " << minSideLength << endl;
// }
// }
for (int i = 0; i < uniformRefinements; i++)
refinementStrategy.hRefineUniformly(mesh);
double nonlinearRelativeEnergyTolerance = 1e-5; // used to determine convergence of the nonlinear solution
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
double L2Update = 1e10;
int iterCount = 0;
while (L2Update > nonlinearRelativeEnergyTolerance && iterCount < maxNewtonIterations)
{
solution->solve(false);
double u1L2Update = solution->L2NormOfSolutionGlobal(u1->ID());
double u2L2Update = solution->L2NormOfSolutionGlobal(u2->ID());
L2Update = sqrt(u1L2Update*u1L2Update + u2L2Update*u2L2Update);
double energy_error = solution->energyErrorTotal();
// Check local conservation
if (commRank == 0)
{
FunctionPtr n = Function::normal();
FunctionPtr u1_prev = Function::solution(u1hat, solution);
FunctionPtr u2_prev = Function::solution(u2hat, solution);
FunctionPtr flux = u1_prev*n->x() + u2_prev*n->y();
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, mesh);
// cout << "Mass flux: Largest Local = " << fluxImbalances[0]
// << ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
errOut << mesh->numGlobalDofs() << " " << energy_error << " "
<< fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;
double massFlux0 = computeFluxOverElementSides(u1_prev, mesh, cellFace0);
double massFlux1 = computeFluxOverElementSides(u1_prev, mesh, cellFace1);
double massFlux2 = computeFluxOverElementSides(u1_prev, mesh, cellFace2);
double massFlux3 = computeFluxOverElementSides(u1_prev, mesh, cellFace3);
double massFlux4 = computeFluxOverElementSides(u1_prev, mesh, cellFace4);
fluxOut << massFlux0 << " " << massFlux1 << " " << massFlux2 << " " << massFlux3 << " " << massFlux4 << " " << endl;
cout << "Total mass flux = " << massFlux0 << " " << massFlux1 << " " << massFlux2 << " " << massFlux3 << " " << massFlux4 << " " << endl;
// if (saveFile.length() > 0) {
// std::ostringstream oss;
// oss << string(saveFile) << refIndex ;
// cout << "on refinement " << refIndex << " saving mesh file to " << oss.str() << endl;
// refHistory->saveToFile(oss.str());
// }
}
// line search algorithm
double alpha = 1.0;
// bool useLineSearch = false;
// int posEnrich = 5; // amount of enriching of grid points on which to ensure positivity
// if (useLineSearch){ // to enforce positivity of density rho
// double lineSearchFactor = .5; double eps = .001; // arbitrary
// FunctionPtr rhoTemp = Function::solution(rho,backgroundFlow) + alpha*Function::solution(rho,solution) - Function::constant(eps);
// FunctionPtr eTemp = Function::solution(e,backgroundFlow) + alpha*Function::solution(e,solution) - Function::constant(eps);
// bool rhoIsPositive = rhoTemp->isPositive(mesh,posEnrich);
// bool eIsPositive = eTemp->isPositive(mesh,posEnrich);
// int iter = 0; int maxIter = 20;
// while (!(rhoIsPositive && eIsPositive) && iter < maxIter){
// alpha = alpha*lineSearchFactor;
// rhoTemp = Function::solution(rho,backgroundFlow) + alpha*Function::solution(rho,solution);
// eTemp = Function::solution(e,backgroundFlow) + alpha*Function::solution(e,solution);
// rhoIsPositive = rhoTemp->isPositive(mesh,posEnrich);
// eIsPositive = eTemp->isPositive(mesh,posEnrich);
// iter++;
// }
// if (commRank==0 && alpha < 1.0){
// cout << "line search factor alpha = " << alpha << endl;
// }
// }
backgroundFlow->addSolution(solution, alpha, false, true);
iterCount++;
// if (commRank == 0)
// cout << "L2 Norm of Update = " << L2Update << endl;
}
if (commRank == 0)
cout << endl;
if (commRank == 0)
{
stringstream outfile;
outfile << "stokeshemker" << uniformRefinements << "_" << refIndex;
exporter.exportSolution(outfile.str());
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
if (commRank == 0)
{
errOut.close();
fluxOut.close();
}
return 0;
}
int main(int argc, char *argv[]) {
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
double epsilon = args.Input<double>("--epsilon", "diffusion parameter");
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = modified robust");
// Optional arguments (have defaults)
halfwidth = args.Input("--halfwidth", "half the width of the wedge", 0.5);
bool allQuads = args.Input("--allQuads", "use only quads in mesh", false);
bool zeroL2 = args.Input("--zeroL2", "take L2 term on v in robust norm to zero", enforceLocalConservation);
args.Process();
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("uhat");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma = varFactory.fieldVar("sigma", VECTOR_L2);
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma / epsilon, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
// Graph norm
if (norm == 0)
{
ip = bf->graphNorm();
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
ip->addZeroMeanTerm( h2_scaling*v );
}
// Robust norm
else if (norm == 1)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
// Weight these two terms for inflow
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
// Modified robust norm
else if (norm == 2)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
ip->addTerm( tau->div() - beta*v->grad() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
SpatialFilterPtr inflow = Teuchos::rcp( new Inflow );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
bc->addDirichlet(beta_n_u_minus_sigma_n, inflow, zero);
SpatialFilterPtr leadingWedge = Teuchos::rcp( new LeadingWedge );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
bc->addDirichlet(uhat, leadingWedge, one);
SpatialFilterPtr trailingWedge = Teuchos::rcp( new TrailingWedge );
bc->addDirichlet(beta_n_u_minus_sigma_n, trailingWedge, beta*n*one);
// bc->addDirichlet(uhat, trailingWedge, one);
SpatialFilterPtr top = Teuchos::rcp( new Top );
bc->addDirichlet(uhat, top, zero);
// bc->addDirichlet(beta_n_u_minus_sigma_n, top, zero);
SpatialFilterPtr outflow = Teuchos::rcp( new Outflow );
pc->addConstraint(beta*uhat->times_normal() - beta_n_u_minus_sigma_n == zero, outflow);
//////////////////// BUILD MESH ///////////////////////
int H1Order = 3, pToAdd = 2;
// define nodes for mesh
vector< FieldContainer<double> > vertices;
FieldContainer<double> pt(2);
vector< vector<int> > elementIndices;
vector<int> q(4);
vector<int> t(3);
if (allQuads)
{
pt(0) = -halfwidth; pt(1) = -1;
vertices.push_back(pt);
pt(0) = 0; pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth; pt(1) = -1;
vertices.push_back(pt);
pt(0) = halfwidth; pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = 0; pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth; pt(1) = halfwidth;
vertices.push_back(pt);
q[0] = 0; q[1] = 1; q[2] = 4; q[3] = 5;
elementIndices.push_back(q);
q[0] = 1; q[1] = 2; q[2] = 3; q[3] = 4;
elementIndices.push_back(q);
}
else
{
pt(0) = -halfwidth; pt(1) = -1;
vertices.push_back(pt);
pt(0) = 0; pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth; pt(1) = -1;
vertices.push_back(pt);
pt(0) = halfwidth; pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth; pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = 0; pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth; pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth; pt(1) = 0;
vertices.push_back(pt);
t[0] = 0; t[1] = 1; t[2] = 7;
elementIndices.push_back(t);
t[0] = 1; t[1] = 2; t[2] = 3;
elementIndices.push_back(t);
q[0] = 1; q[1] = 3; q[2] = 4; q[3] = 5;
elementIndices.push_back(q);
q[0] = 7; q[1] = 1; q[2] = 5; q[3] = 6;
elementIndices.push_back(q);
}
Teuchos::RCP<Mesh> mesh = Teuchos::rcp( new Mesh(vertices, elementIndices, bf, H1Order, pToAdd) );
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->setFilter(pc);
if (enforceLocalConservation) {
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(solution, mesh, varFactory);
ofstream errOut;
if (commRank == 0)
errOut.open("singularwedge_err.txt");
for (int refIndex=0; refIndex<=numRefs; refIndex++){
solution->solve(false);
double energy_error = solution->energyErrorTotal();
if (commRank==0){
stringstream outfile;
outfile << "singularwedge_" << refIndex;
exporter.exportSolution(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_sigma_n) );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
errOut << mesh->numGlobalDofs() << " " << energy_error << " "
<< fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
if (commRank == 0)
errOut.close();
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("uhat");
VarPtr sigma_n = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("sigma1");
VarPtr sigma2 = varFactory.fieldVar("sigma2");
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma1, tau->x());
bf->addTerm(sigma2, tau->y());
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma1, v->dx() );
bf->addTerm( sigma2, v->dy() );
bf->addTerm( -sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(1.0) );
rhs->addTerm( f * v );
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
SpatialFilterPtr inflow = Teuchos::rcp( new Inflow );
bc->addDirichlet(uhat, inflow, zero);
SpatialFilterPtr leadingWedge = Teuchos::rcp( new LeadingWedge );
bc->addDirichlet(uhat, leadingWedge, zero);
SpatialFilterPtr trailingWedge = Teuchos::rcp( new TrailingWedge );
bc->addDirichlet(sigma_n, trailingWedge, zero);
// bc->addDirichlet(uhat, trailingWedge, zero);
SpatialFilterPtr top = Teuchos::rcp( new Top );
bc->addDirichlet(uhat, top, zero);
SpatialFilterPtr outflow = Teuchos::rcp( new Outflow );
bc->addDirichlet(uhat, outflow, zero);
//////////////////// BUILD MESH ///////////////////////
bool allQuads = true;
int H1Order = 3, pToAdd = 2;
// define nodes for mesh
vector< FieldContainer<double> > vertices;
FieldContainer<double> pt(2);
vector< vector<int> > elementIndices;
vector<int> q(4);
vector<int> t(3);
if (allQuads)
{
pt(0) = -halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
q[0] = 0;
q[1] = 1;
q[2] = 4;
q[3] = 5;
elementIndices.push_back(q);
q[0] = 1;
q[1] = 2;
q[2] = 3;
q[3] = 4;
elementIndices.push_back(q);
}
else
{
pt(0) = -halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth;
pt(1) = 0;
vertices.push_back(pt);
t[0] = 0;
t[1] = 1;
t[2] = 7;
elementIndices.push_back(t);
t[0] = 1;
t[1] = 2;
t[2] = 3;
elementIndices.push_back(t);
q[0] = 1;
q[1] = 3;
q[2] = 4;
q[3] = 5;
elementIndices.push_back(q);
q[0] = 7;
q[1] = 1;
q[2] = 5;
q[3] = 6;
elementIndices.push_back(q);
}
Teuchos::RCP<Mesh> mesh = Teuchos::rcp( new Mesh(vertices, elementIndices, bf, H1Order, pToAdd) );
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->setFilter(pc);
if (enforceLocalConservation)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(sigma_n == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
solution->solve(false);
if (rank==0)
{
stringstream outfile;
outfile << "poissonwedge_" << refIndex;
solution->writeToVTK(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma_n) );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
if (refIndex < numRefs)
{
// refinementStrategy.refine(rank==0); // print to console on rank 0
vector<int> cellsToRefine;
vector<int> cells_h;
vector<int> cells_p;
refinementStrategy.getCellsAboveErrorThreshhold(cellsToRefine);
for (int i=0; i < cellsToRefine.size(); i++)
if (sqrt(mesh->getCellMeasure(cellsToRefine[i])) < 1e-3)
{
int pOrder = mesh->cellPolyOrder(cellsToRefine[i]);
if (allQuads)
cells_p.push_back(cellsToRefine[i]);
else if (pOrder < 8)
cells_p.push_back(cellsToRefine[i]);
else
cout << "Reached cell size and polynomial order limits" << endl;
// cells_h.push_back(cellsToRefine[i]);
}
else
cells_h.push_back(cellsToRefine[i]);
refinementStrategy.pRefineCells(mesh, cells_p);
refinementStrategy.hRefineCells(mesh, cells_h);
}
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
bool steady = args.Input<bool>("--steady", "run steady rather than transient");
// Optional arguments (have defaults)
double dt = args.Input("--dt", "time step", 0.25);
int numTimeSteps = args.Input("--nt", "number of time steps", 20);
halfWidth = args.Input("--halfWidth", "half width of inlet profile", 1.0);
args.Process();
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr beta_n_u_hat = varFactory.fluxVar("\\widehat{\\beta \\cdot n }");
VarPtr u = varFactory.fieldVar("u");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
meshBoundary(0,0) = 0.0; // x1
meshBoundary(0,1) = -2.0; // y1
meshBoundary(1,0) = 4.0;
meshBoundary(1,1) = -2.0;
meshBoundary(2,0) = 4.0;
meshBoundary(2,1) = 2.0;
meshBoundary(3,0) = 0.0;
meshBoundary(3,1) = 2.0;
int horizontalCells = 8, verticalCells = 8;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
bf, H1Order, H1Order+pToAdd);
////////////////////////////////////////////////////////////////////
// INITIALIZE FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr prevTimeFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
SolutionPtr flowResidual = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
FunctionPtr u_prev_time = Teuchos::rcp( new PreviousSolutionFunction(prevTimeFlow, u) );
//////////////////// DEFINE BILINEAR FORM ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr invDt = Teuchos::rcp(new ScalarParamFunction(1.0/dt));
// v terms:
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( beta_n_u_hat, v);
if (!steady)
{
bf->addTerm( u, invDt*v );
rhs->addTerm( u_prev_time * invDt * v );
}
//////////////////// SPECIFY RHS ///////////////////////
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
// ip->addTerm(v);
// ip->addTerm(beta*v->grad());
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr lBoundary = Teuchos::rcp( new LeftBoundary );
FunctionPtr u1 = Teuchos::rcp( new InletBC );
bc->addDirichlet(beta_n_u_hat, lBoundary, -u1);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(prevTimeFlow);
mesh->registerSolution(flowResidual);
// ==================== SET INITIAL GUESS ==========================
double u_free = 0.0;
map<int, Teuchos::RCP<Function> > functionMap;
// functionMap[u->ID()] = Teuchos::rcp( new ConInletBC
functionMap[u->ID()] = Teuchos::rcp( new InletBC );
prevTimeFlow->projectOntoMesh(functionMap);
//////////////////// SOLVE & REFINE ///////////////////////
if (enforceLocalConservation)
{
if (steady)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_hat == zero);
}
else
{
// FunctionPtr parity = Teuchos::rcp<Function>( new SideParityFunction );
// LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(parity, beta_n_u_minus_sigma_n) );
LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(1.0, beta_n_u_hat) );
LinearTermPtr sourcePart = Teuchos::rcp<LinearTerm>( new LinearTerm(invDt, u) );
conservedQuantity->addTerm(sourcePart, true);
solution->lagrangeConstraints()->addConstraint(conservedQuantity == u_prev_time * invDt);
}
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(solution, mesh, varFactory);
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
if (steady)
{
solution->solve(false);
if (commRank == 0)
{
stringstream outfile;
outfile << "Convection_" << refIndex;
exporter.exportSolution(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
}
else
{
int timestepCount = 0;
double time_tol = 1e-8;
double L2_time_residual = 1e9;
// cout << L2_time_residual <<" "<< time_tol << timestepCount << numTimeSteps << endl;
while((L2_time_residual > time_tol) && (timestepCount < numTimeSteps))
{
solution->solve(false);
// Subtract solutions to get residual
flowResidual->setSolution(solution);
flowResidual->addSolution(prevTimeFlow, -1.0);
L2_time_residual = flowResidual->L2NormOfSolutionGlobal(u->ID());
if (commRank == 0)
{
cout << endl << "Timestep: " << timestepCount << ", dt = " << dt << ", Time residual = " << L2_time_residual << endl;
stringstream outfile;
outfile << "TransientConvection_" << refIndex << "-" << timestepCount;
exporter.exportSolution(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
FunctionPtr source = Teuchos::rcp( new PreviousSolutionFunction(flowResidual, u) );
source = -invDt * source;
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, source, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
prevTimeFlow->setSolution(solution); // reset previous time solution to current time sol
timestepCount++;
}
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
double epsilon = args.Input<double>("--epsilon", "diffusion parameter");
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
bool graphNorm = args.Input<bool>("--graphNorm", "use the graph norm rather than robust test norm");
// Optional arguments (have defaults)
bool highLiftAirfoil = args.Input("--highLift", "use high lift airfoil rather than NACA0012", false);
args.Process();
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("uhat");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma = varFactory.fieldVar("sigma", VECTOR_L2);
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.25);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma / epsilon, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (graphNorm)
{
ip = bf->graphNorm();
}
else
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
if (!enforceLocalConservation)
ip->addTerm( ip_scaling * v );
ip->addTerm( sqrt(epsilon) * v->grad() );
// Weight these two terms for inflow
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (enforceLocalConservation)
ip->addZeroMeanTerm( v );
}
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
SpatialFilterPtr lBoundary = Teuchos::rcp( new LeftBoundary );
SpatialFilterPtr tBoundary = Teuchos::rcp( new TopBoundary );
SpatialFilterPtr bBoundary = Teuchos::rcp( new BottomBoundary );
SpatialFilterPtr rBoundary = Teuchos::rcp( new RightBoundary );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
SpatialFilterPtr airfoilInflowBoundary = Teuchos::rcp( new AirfoilInflowBoundary(beta) );
SpatialFilterPtr airfoilOutflowBoundary = Teuchos::rcp( new AirfoilOutflowBoundary(beta) );
FunctionPtr u0 = Teuchos::rcp( new ZeroBC );
FunctionPtr u1 = Teuchos::rcp( new OneBC );
bc->addDirichlet(beta_n_u_minus_sigma_n, lBoundary, u0);
bc->addDirichlet(beta_n_u_minus_sigma_n, bBoundary, u0);
// bc->addDirichlet(uhat, airfoilInflowBoundary, u1);
// bc->addDirichlet(uhat, tBoundary, u0);
bc->addDirichlet(beta_n_u_minus_sigma_n, airfoilInflowBoundary, beta*n*u1);
bc->addDirichlet(uhat, airfoilOutflowBoundary, u1);
// pc->addConstraint(beta*uhat->times_normal() - beta_n_u_minus_sigma_n == u0, rBoundary);
// pc->addConstraint(beta*uhat->times_normal() - beta_n_u_minus_sigma_n == u0, tBoundary);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 3, pToAdd = 2;
Teuchos::RCP<Mesh> mesh;
if (highLiftAirfoil)
mesh = Mesh::readTriangle(Camellia_MeshDir+"HighLift/HighLift.1", bf, H1Order, pToAdd);
else
mesh = Mesh::readTriangle(Camellia_MeshDir+"NACA0012/NACA0012.1", bf, H1Order, pToAdd);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
// solution->setFilter(pc);
if (enforceLocalConservation)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(solution, mesh, varFactory);
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
solution->solve(false);
if (commRank == 0)
{
stringstream outfile;
if (highLiftAirfoil)
outfile << "highlift_" << refIndex;
else
outfile << "naca0012_" << refIndex;
exporter.exportSolution(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_sigma_n) );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
if (refIndex < numRefs)
{
// refinementStrategy.refine(commRank==0); // print to console on commRank 0
// Try pseudo-hp adaptive
vector<int> cellsToRefine;
vector<int> cells_h;
vector<int> cells_p;
refinementStrategy.getCellsAboveErrorThreshhold(cellsToRefine);
for (int i=0; i < cellsToRefine.size(); i++)
if (sqrt(mesh->getCellMeasure(cellsToRefine[i])) < epsilon)
{
int pOrder = mesh->cellPolyOrder(cellsToRefine[i]);
if (pOrder < 8)
cells_p.push_back(cellsToRefine[i]);
else
cells_h.push_back(cellsToRefine[i]);
}
else
cells_h.push_back(cellsToRefine[i]);
refinementStrategy.pRefineCells(mesh, cells_p);
refinementStrategy.hRefineCells(mesh, cells_h);
}
}
return 0;
}
int main(int argc, char *argv[]) {
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
double epsilon = args.Input<double>("--epsilon", "diffusion parameter");
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = modified robust");
// Optional arguments (have defaults)
bool zeroL2 = args.Input("--zeroL2", "take L2 term on v in robust norm to zero", true);
args.Process();
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("uhat");
VarPtr fhat = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma = varFactory.fieldVar("sigma", VECTOR_L2);
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
int H1Order = 3, pToAdd = 2;
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
meshBoundary(0,0) = 0.0; // x1
meshBoundary(0,1) = 0.0; // y1
meshBoundary(1,0) = 1.0;
meshBoundary(1,1) = 0.0;
meshBoundary(2,0) = 1.0;
meshBoundary(2,1) = 1.0;
meshBoundary(3,0) = 0.0;
meshBoundary(3,1) = 1.0;
int horizontalCells = 4, verticalCells = 4;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
bf, H1Order, H1Order+pToAdd, false);
vector<double> beta;
beta.push_back(2.0);
beta.push_back(1.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
// tau terms:
bf->addTerm(sigma / epsilon, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( fhat, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (norm == 0)
{
ip = bf->graphNorm();
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
ip->addZeroMeanTerm( h2_scaling*v );
}
// Robust norm
else if (norm == 1)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
// Weight these two terms for inflow
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
// Modified robust norm
else if (norm == 2)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
// FunctionPtr ip_weight = Teuchos::rcp( new IPWeight() );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() - beta*v->grad() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowBoundary );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowBoundary );
FunctionPtr u0 = Teuchos::rcp( new U0 );
bc->addDirichlet(uhat, outflowBoundary, u0);
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
bc->addDirichlet(fhat, inflowBoundary, beta*n*u0);
// Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints);
// pc->addConstraint(uhat==u0,inflowBoundary);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
// solution->setFilter(pc);
if (enforceLocalConservation) {
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(fhat == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(solution, mesh, varFactory);
ofstream errOut;
if (commRank == 0)
errOut.open("confusion_err.txt");
for (int refIndex=0; refIndex<=numRefs; refIndex++){
solution->solve(false);
double energy_error = solution->energyErrorTotal();
if (commRank==0){
stringstream outfile;
outfile << "confusion_" << refIndex;
exporter.exportSolution(outfile.str());
// solution->writeToVTK(outfile.str());
// Check local conservation
FunctionPtr flux = Function::solution(fhat, solution);
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
errOut << mesh->numGlobalDofs() << " " << energy_error << " "
<< fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
if (commRank == 0)
errOut.close();
return 0;
}
