diff --git a/test/freeflow/navierstokes/CMakeLists.txt b/test/freeflow/navierstokes/CMakeLists.txt
index 70746e33d2d3b0cb5819f21fc369868f924ff776..70806b5004121dcbfa60ec263f6f4d3cc65ef422 100644
--- a/test/freeflow/navierstokes/CMakeLists.txt
+++ b/test/freeflow/navierstokes/CMakeLists.txt
@@ -3,5 +3,6 @@ add_subdirectory(angeli)
add_subdirectory(kovasznay)
add_subdirectory(closedsystem)
add_subdirectory(channel)
+add_subdirectory(sincos)
dune_symlink_to_source_files(FILES convergence.sh)
diff --git a/test/freeflow/navierstokes/sincos/CMakeLists.txt b/test/freeflow/navierstokes/sincos/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b2cb92fb0913aefb7956e7c81d8c79fdaedea335
--- /dev/null
+++ b/test/freeflow/navierstokes/sincos/CMakeLists.txt
@@ -0,0 +1,29 @@
+dune_symlink_to_source_files(FILES "convergencetest.py")
+dune_symlink_to_source_files(FILES "params.input")
+
+dune_add_test(NAME test_ff_navierstokes_sincos
+ SOURCES main.cc
+ LABELS freeflow
+ CMAKE_GUARD HAVE_UMFPACK
+ COMMAND ./convergencetest.py
+ CMD_ARGS test_ff_navierstokes_sincos params.input
+ -Grid.UpperRight "6.28 6.28"
+ -Grid.Cells "150 150"
+ -Problem.Name test_ff_navierstokes_sincos_stationary_convergence
+ -Problem.IsStationary true
+ -Component.LiquidKinematicViscosity 0.001)
+
+dune_add_test(NAME test_ff_navierstokes_sincos_instationary
+ TARGET test_ff_navierstokes_sincos
+ LABELS freeflow
+ CMAKE_GUARD HAVE_UMFPACK
+ COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+ CMD_ARGS --script fuzzy
+ --files ${CMAKE_SOURCE_DIR}/test/references/test_ff_navierstokes_sincos_instationary-reference.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_ff_navierstokes_sincos_instationary-00017.vtu
+ --command "${CMAKE_CURRENT_BINARY_DIR}/test_ff_navierstokes_sincos params.input
+ -Grid.UpperRight '1 1'
+ -Grid.Cells '50 50'
+ -Problem.Name test_ff_navierstokes_sincos_instationary
+ -Problem.IsStationary false
+ -Component.LiquidKinematicViscosity 0.1")
diff --git a/test/freeflow/navierstokes/sincos/convergencetest.py b/test/freeflow/navierstokes/sincos/convergencetest.py
new file mode 100755
index 0000000000000000000000000000000000000000..7ca61e01b69aab48af278c17b34fd83e64b2f9bd
--- /dev/null
+++ b/test/freeflow/navierstokes/sincos/convergencetest.py
@@ -0,0 +1,79 @@
+#!/usr/bin/env python
+
+from math import *
+import subprocess
+import sys
+import numpy
+
+if len(sys.argv) < 2:
+ sys.stderr.write('Please provide a single argument <testname> to the script\n')
+ sys.exit(1)
+
+testname = str(sys.argv[1])
+testargs = [str(i) for i in sys.argv][2:]
+
+# remove the old log file
+subprocess.call(['rm', testname + '.log'])
+print("Removed old log file ({})!".format(testname + '.log'))
+
+# do the runs with different refinement
+for i in [0, 1]:
+ subprocess.call(['./' + testname] + testargs + ['-Grid.Refinement', str(i),
+ '-Problem.Name', testname])
+
+# check the rates and append them to the log file
+logfile = open(testname + '.log', "r+")
+
+errorP = []
+errorVx = []
+errorVy = []
+for line in logfile:
+ line = line.strip("\n")
+ line = line.strip("\[ConvergenceTest\]")
+ line = line.split()
+ errorP.append(float(line[2]))
+ errorVx.append(float(line[5]))
+ errorVy.append(float(line[8]))
+
+resultsP = []
+resultsVx = []
+resultsVy = []
+logfile.truncate(0)
+logfile.write("n\terrorP\t\trateP\t\terrorVx\t\trateVx\t\terrorVy\t\trateVy\n")
+logfile.write("-"*50 + "\n")
+for i in range(len(errorP)-1):
+ if isnan(errorP[i]) or isinf(errorP[i]):
+ continue
+ if not ((errorP[i] < 1e-12 or errorP[i+1] < 1e-12) and (errorVx[i] < 1e-12 or errorVx[i+1] < 1e-12) and (errorVy[i] < 1e-12 or errorVy[i+1] < 1e-12)):
+ rateP = (log(errorP[i])-log(errorP[i+1]))/log(2)
+ rateVx = (log(errorVx[i])-log(errorVx[i+1]))/log(2)
+ rateVy = (log(errorVy[i])-log(errorVy[i+1]))/log(2)
+ message = "{}\t{:0.4e}\t{:0.4e}\t{:0.4e}\t{:0.4e}\t{:0.4e}\t{:0.4e}\n".format(i, errorP[i], rateP, errorVx[i], rateVx, errorVy[i], rateVy)
+ logfile.write(message)
+ resultsP.append(rateP)
+ resultsVx.append(rateVx)
+ resultsVy.append(rateVy)
+ else:
+ logfile.write("error: exact solution!?")
+i = len(errorP)-1
+message = "{}\t{:0.4e}\t\t{}\t{:0.4e}\t\t{}\t{:0.4e}\t\t{}\n".format(i, errorP[i], "", errorVx[i], "", errorVy[i], "")
+logfile.write(message)
+
+logfile.close()
+print("\nComputed the following convergence rates for {}:\n".format(testname))
+subprocess.call(['cat', testname + '.log'])
+
+# check the rates, we expect rates around 2
+if int(numpy.mean(resultsP) < 2.05 and numpy.mean(resultsP) < 1.95):
+ sys.stderr.write("*"*70 + "\n" + "The convergence rates for pressure were not close enough to 2! Test failed.\n" + "*"*70 + "\n")
+ sys.exit(1)
+
+if int(numpy.mean(resultsVx) < 2.05 and numpy.mean(resultsVx) < 1.95):
+ sys.stderr.write("*"*70 + "\n" + "The convergence rates for x-velocity were not close enough to 2! Test failed.\n" + "*"*70 + "\n")
+ sys.exit(1)
+
+if int(numpy.mean(resultsVy) < 2.05 and numpy.mean(resultsVy) < 1.95):
+ sys.stderr.write("*"*70 + "\n" + "The convergence rates for y-velocity were not close enough to 2! Test failed.\n" + "*"*70 + "\n")
+ sys.exit(1)
+
+sys.exit(0)
diff --git a/test/freeflow/navierstokes/sincos/main.cc b/test/freeflow/navierstokes/sincos/main.cc
new file mode 100644
index 0000000000000000000000000000000000000000..7ac6fe787affcbea0f3816e48597e96f9657500b
--- /dev/null
+++ b/test/freeflow/navierstokes/sincos/main.cc
@@ -0,0 +1,361 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ * See the file COPYING for full copying permissions. *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 3 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup NavierStokesTests
+ * \brief Test for the instationary staggered grid Navier-Stokes model
+ * with analytical solution.
+ */
+
+#include <config.h>
+
+#include <ctime>
+#include <iostream>
+#include <type_traits>
+#include <tuple>
+
+#include <dune/common/parallel/mpihelper.hh>
+#include <dune/common/timer.hh>
+#include <dune/grid/io/file/dgfparser/dgfexception.hh>
+#include <dune/grid/io/file/vtk.hh>
+
+#include <dumux/assembly/staggeredfvassembler.hh>
+#include <dumux/assembly/diffmethod.hh>
+#include <dumux/common/dumuxmessage.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/properties.hh>
+#include <dumux/common/valgrind.hh>
+#include <dumux/io/grid/gridmanager.hh>
+#include <dumux/io/staggeredvtkoutputmodule.hh>
+#include <dumux/linear/seqsolverbackend.hh>
+#include <dumux/nonlinear/newtonsolver.hh>
+
+#include "problem.hh"
+
+/*!
+* \brief Creates analytical solution.
+* Returns a tuple of the analytical solution for the pressure, the velocity and the velocity at the faces
+* \param time the time at which to evaluate the analytical solution
+* \param problem the problem for which to evaluate the analytical solution
+*/
+template<class Scalar, class Problem>
+auto createAnalyticalSolution(const Scalar time, const Problem& problem)
+{
+ const auto& fvGridGeometry = problem.fvGridGeometry();
+ using GridView = typename std::decay_t<decltype(fvGridGeometry)>::GridView;
+
+ static constexpr auto dim = GridView::dimension;
+ static constexpr auto dimWorld = GridView::dimensionworld;
+
+ using VelocityVector = Dune::FieldVector<Scalar, dimWorld>;
+
+ std::vector<Scalar> analyticalPressure;
+ std::vector<VelocityVector> analyticalVelocity;
+ std::vector<VelocityVector> analyticalVelocityOnFace;
+
+ analyticalPressure.resize(fvGridGeometry.numCellCenterDofs());
+ analyticalVelocity.resize(fvGridGeometry.numCellCenterDofs());
+ analyticalVelocityOnFace.resize(fvGridGeometry.numFaceDofs());
+
+ using Indices = typename Problem::Indices;
+ for (const auto& element : elements(fvGridGeometry.gridView()))
+ {
+ auto fvGeometry = localView(fvGridGeometry);
+ fvGeometry.bindElement(element);
+ for (auto&& scv : scvs(fvGeometry))
+ {
+ auto ccDofIdx = scv.dofIndex();
+ auto ccDofPosition = scv.dofPosition();
+ auto analyticalSolutionAtCc = problem.analyticalSolution(ccDofPosition, time);
+
+ // velocities on faces
+ for (auto&& scvf : scvfs(fvGeometry))
+ {
+ const auto faceDofIdx = scvf.dofIndex();
+ const auto faceDofPosition = scvf.center();
+ const auto dirIdx = scvf.directionIndex();
+ const auto analyticalSolutionAtFace = problem.analyticalSolution(faceDofPosition, time);
+ analyticalVelocityOnFace[faceDofIdx][dirIdx] = analyticalSolutionAtFace[Indices::velocity(dirIdx)];
+ }
+
+ analyticalPressure[ccDofIdx] = analyticalSolutionAtCc[Indices::pressureIdx];
+
+ for(int dirIdx = 0; dirIdx < dim; ++dirIdx)
+ analyticalVelocity[ccDofIdx][dirIdx] = analyticalSolutionAtCc[Indices::velocity(dirIdx)];
+ }
+ }
+
+ return std::make_tuple(analyticalPressure, analyticalVelocity, analyticalVelocityOnFace);
+}
+
+template<class Problem>
+auto createSource(const Problem& problem)
+{
+ using Scalar = double;
+ using Indices = typename Problem::Indices;
+
+ const auto& fvGridGeometry = problem.fvGridGeometry();
+ std::array<std::vector<Scalar>, Problem::ModelTraits::numEq()> source;
+
+ for (auto& component : source)
+ {
+ component.resize(fvGridGeometry.numCellCenterDofs());
+ }
+
+ for (const auto& element : elements(fvGridGeometry.gridView()))
+ {
+ auto fvGeometry = localView(fvGridGeometry);
+ fvGeometry.bindElement(element);
+ for (auto&& scv : scvs(fvGeometry))
+ {
+ auto ccDofIdx = scv.dofIndex();
+ auto ccDofPosition = scv.dofPosition();
+
+ auto sourceAtPosVal = problem.sourceAtPos(ccDofPosition);
+
+ source[Indices::momentumXBalanceIdx][ccDofIdx] = sourceAtPosVal[Indices::momentumXBalanceIdx];
+ source[Indices::momentumYBalanceIdx][ccDofIdx] = sourceAtPosVal[Indices::momentumYBalanceIdx];
+ }
+ }
+
+ return source;
+}
+
+template<class Problem, class SolutionVector, class FVGridGeometry>
+void printL2Error(const Problem& problem, const SolutionVector& x, const FVGridGeometry& fvGridGeometry)
+{
+ using namespace Dumux;
+ using Scalar = double;
+ using TypeTag = Properties::TTag::SincosTest;
+ using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
+ using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
+ using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+
+ using L2Error = NavierStokesTestL2Error<Scalar, ModelTraits, PrimaryVariables>;
+ const auto l2error = L2Error::calculateL2Error(*problem, x);
+ const int numCellCenterDofs = fvGridGeometry->numCellCenterDofs();
+ const int numFaceDofs = fvGridGeometry->numFaceDofs();
+ std::cout << std::setprecision(8) << "** L2 error (abs/rel) for "
+ << std::setw(6) << numCellCenterDofs << " cc dofs and " << numFaceDofs << " face dofs (total: " << numCellCenterDofs + numFaceDofs << "): "
+ << std::scientific
+ << "L2(p) = " << l2error.first[Indices::pressureIdx] << " / " << l2error.second[Indices::pressureIdx]
+ << " , L2(vx) = " << l2error.first[Indices::velocityXIdx] << " / " << l2error.second[Indices::velocityXIdx]
+ << " , L2(vy) = " << l2error.first[Indices::velocityYIdx] << " / " << l2error.second[Indices::velocityYIdx]
+ << std::endl;
+
+ // write the norm into a log file
+ std::ofstream logFile;
+ logFile.open(problem->name() + ".log", std::ios::app);
+ logFile << "[ConvergenceTest] L2(p) = " << l2error.first[Indices::pressureIdx] << " L2(vx) = " << l2error.first[Indices::velocityXIdx] << " L2(vy) = " << l2error.first[Indices::velocityYIdx] << std::endl;
+ logFile.close();
+}
+
+int main(int argc, char** argv) try
+{
+ using namespace Dumux;
+
+ // define the type tag for this problem
+ using TypeTag = Properties::TTag::SincosTest;
+
+ // initialize MPI, finalize is done automatically on exit
+ const auto& mpiHelper = Dune::MPIHelper::instance(argc, argv);
+
+ // print dumux start message
+ if (mpiHelper.rank() == 0)
+ DumuxMessage::print(/*firstCall=*/true);
+
+ // parse command line arguments and input file
+ Parameters::init(argc, argv);
+
+ // try to create a grid (from the given grid file or the input file)
+ GridManager<GetPropType<TypeTag, Properties::Grid>> gridManager;
+ gridManager.init();
+
+ ////////////////////////////////////////////////////////////
+ // run instationary non-linear problem on this grid
+ ////////////////////////////////////////////////////////////
+
+ // we compute on the leaf grid view
+ const auto& leafGridView = gridManager.grid().leafGridView();
+
+ // create the finite volume grid geometry
+ using FVGridGeometry = GetPropType<TypeTag, Properties::FVGridGeometry>;
+ auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
+ fvGridGeometry->update();
+
+ // get some time loop parameters
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ const auto tEnd = getParam<Scalar>("TimeLoop.TEnd");
+ const auto maxDt = getParam<Scalar>("TimeLoop.MaxTimeStepSize");
+ auto dt = getParam<Scalar>("TimeLoop.DtInitial");
+
+ // instantiate time loop
+ auto timeLoop = std::make_shared<TimeLoop<Scalar>>(0.0, dt, tEnd);
+ timeLoop->setMaxTimeStepSize(maxDt);
+
+ // the problem (initial and boundary conditions)
+ using Problem = GetPropType<TypeTag, Properties::Problem>;
+ auto problem = std::make_shared<Problem>(fvGridGeometry);
+ problem->updateTimeStepSize(timeLoop->timeStepSize());
+
+ // the solution vector
+ using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+ SolutionVector x;
+ x[FVGridGeometry::cellCenterIdx()].resize(fvGridGeometry->numCellCenterDofs());
+ x[FVGridGeometry::faceIdx()].resize(fvGridGeometry->numFaceDofs());
+ problem->applyInitialSolution(x);
+ auto xOld = x;
+
+ // the grid variables
+ using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+ auto gridVariables = std::make_shared<GridVariables>(problem, fvGridGeometry);
+ gridVariables->init(x);
+
+ // initialize the vtk output module
+ StaggeredVtkOutputModule<GridVariables, SolutionVector> vtkWriter(*gridVariables, x, problem->name());
+ using IOFields = GetPropType<TypeTag, Properties::IOFields>;
+ IOFields::initOutputModule(vtkWriter); // Add model specific output fields
+
+ auto source = createSource(*problem);
+ auto sourceX = source[Problem::Indices::momentumXBalanceIdx];
+ auto sourceY = source[Problem::Indices::momentumYBalanceIdx];
+ vtkWriter.addField(sourceX, "sourceX");
+ vtkWriter.addField(sourceY, "sourceY");
+
+ auto analyticalSolution = createAnalyticalSolution(timeLoop->time(), *problem);
+ vtkWriter.addField(std::get<0>(analyticalSolution), "pressureExact");
+ vtkWriter.addField(std::get<1>(analyticalSolution), "velocityExact");
+ vtkWriter.addFaceField(std::get<2>(analyticalSolution), "faceVelocityExact");
+ vtkWriter.write(0.0);
+
+ const bool isStationary = getParam<bool>("Problem.IsStationary");
+
+ // the assembler with time loop for instationary problem
+ using Assembler = StaggeredFVAssembler<TypeTag, DiffMethod::numeric>;
+ auto assembler = isStationary ? std::make_shared<Assembler>(problem, fvGridGeometry, gridVariables) : std::make_shared<Assembler>(problem, fvGridGeometry, gridVariables, timeLoop);
+
+ // the linear solver
+ using LinearSolver = Dumux::UMFPackBackend;
+ auto linearSolver = std::make_shared<LinearSolver>();
+
+ // the non-linear solver
+ using NewtonSolver = Dumux::NewtonSolver<Assembler, LinearSolver>;
+ NewtonSolver nonLinearSolver(assembler, linearSolver);
+
+ const bool shouldPrintL2Error = getParam<bool>("Problem.PrintL2Error");
+
+ if (isStationary)
+ {
+ // linearize & solve
+ Dune::Timer timer;
+ nonLinearSolver.solve(x);
+
+ if (shouldPrintL2Error)
+ {
+ printL2Error(problem, x, fvGridGeometry);
+ }
+
+ // write vtk output
+ analyticalSolution = createAnalyticalSolution(timeLoop->time(), *problem);
+ vtkWriter.write(1.0);
+
+ timer.stop();
+
+ const auto& comm = Dune::MPIHelper::getCollectiveCommunication();
+ std::cout << "Simulation took " << timer.elapsed() << " seconds on "
+ << comm.size() << " processes.\n"
+ << "The cumulative CPU time was " << timer.elapsed()*comm.size() << " seconds.\n";
+ }
+ else
+ {
+ // time loop
+ timeLoop->start(); do
+ {
+ // set previous solution for storage evaluations
+ assembler->setPreviousSolution(xOld);
+
+ // solve the non-linear system with time step control
+ nonLinearSolver.solve(x, *timeLoop);
+
+ // make the new solution the old solution
+ xOld = x;
+ gridVariables->advanceTimeStep();
+
+ if (shouldPrintL2Error)
+ {
+ printL2Error(problem, x, fvGridGeometry);
+ }
+
+ // advance to the time loop to the next step
+ timeLoop->advanceTimeStep();
+ problem->updateTime(timeLoop->time());
+ analyticalSolution = createAnalyticalSolution(timeLoop->time(), *problem);
+
+ // write vtk output
+ vtkWriter.write(timeLoop->time());
+
+ // report statistics of this time step
+ timeLoop->reportTimeStep();
+
+ // set new dt as suggested by newton solver
+ timeLoop->setTimeStepSize(nonLinearSolver.suggestTimeStepSize(timeLoop->timeStepSize()));
+ problem->updateTimeStepSize(timeLoop->timeStepSize());
+
+ } while (!timeLoop->finished());
+
+ timeLoop->finalize(leafGridView.comm());
+ }
+
+ ////////////////////////////////////////////////////////////
+ // finalize, print dumux message to say goodbye
+ ////////////////////////////////////////////////////////////
+
+ // print dumux end message
+ if (mpiHelper.rank() == 0)
+ {
+ Parameters::print();
+ DumuxMessage::print(/*firstCall=*/false);
+ }
+
+ return 0;
+} // end main
+catch (Dumux::ParameterException &e)
+{
+ std::cerr << std::endl << e << " ---> Abort!" << std::endl;
+ return 1;
+}
+catch (Dune::DGFException & e)
+{
+ std::cerr << "DGF exception thrown (" << e <<
+ "). Most likely, the DGF file name is wrong "
+ "or the DGF file is corrupted, "
+ "e.g. missing hash at end of file or wrong number (dimensions) of entries."
+ << " ---> Abort!" << std::endl;
+ return 2;
+}
+catch (Dune::Exception &e)
+{
+ std::cerr << "Dune reported error: " << e << " ---> Abort!" << std::endl;
+ return 3;
+}
+catch (...)
+{
+ std::cerr << "Unknown exception thrown! ---> Abort!" << std::endl;
+ return 4;
+}
diff --git a/test/freeflow/navierstokes/sincos/params.input b/test/freeflow/navierstokes/sincos/params.input
new file mode 100644
index 0000000000000000000000000000000000000000..80f5d2becadc5c3abb0bff3c8bf8cf310fb9afd0
--- /dev/null
+++ b/test/freeflow/navierstokes/sincos/params.input
@@ -0,0 +1,36 @@
+[TimeLoop]
+DtInitial = 0.01 # [s]
+TEnd = 1.0 # [s]
+
+[Grid]
+LowerLeft = 0 0
+UpperRight = 1 1
+
+[Problem]
+Name = test_ff_sincos
+EnableGravity = false
+PrintL2Error = true
+EnableInertiaTerms = true
+IsStationary = false
+
+[Component]
+LiquidDensity = 1.0
+LiquidKinematicViscosity = 0.1
+
+[Assembly]
+NumericDifference.BaseEpsilon = 1e-8
+
+[Newton]
+MaxSteps = 10
+TargetSteps = 4
+MaxRelativeShift = 1e-5
+SatisfyResidualAndShiftCriterion = true
+EnableAbsoluteResidualCriterion = true
+MaxAbsoluteResidual = 1e-10
+
+[Vtk]
+WriteFaceData = false
+AddProcessRank = false
+
+[Flux]
+UpwindWeight = 0.5
diff --git a/test/freeflow/navierstokes/sincos/problem.hh b/test/freeflow/navierstokes/sincos/problem.hh
new file mode 100644
index 0000000000000000000000000000000000000000..3a21c0a1213638de8245e470df51579df4c951fd
--- /dev/null
+++ b/test/freeflow/navierstokes/sincos/problem.hh
@@ -0,0 +1,299 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ * See the file COPYING for full copying permissions. *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 3 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup NavierStokesTests
+ * \brief Test for the staggered grid Navier-Stokes model
+ * with analytical solution.
+ */
+#ifndef DUMUX_SINCOS_TEST_PROBLEM_HH
+#define DUMUX_SINCOS_TEST_PROBLEM_HH
+
+#include <dune/grid/yaspgrid.hh>
+
+#include <dumux/material/fluidsystems/1pliquid.hh>
+#include <dumux/material/components/constant.hh>
+
+#include <dumux/freeflow/navierstokes/problem.hh>
+#include <dumux/discretization/staggered/freeflow/properties.hh>
+#include <dumux/freeflow/navierstokes/model.hh>
+#include "../l2error.hh"
+
+namespace Dumux {
+template <class TypeTag>
+class SincosTestProblem;
+
+namespace Properties {
+// Create new type tags
+namespace TTag {
+struct SincosTest { using InheritsFrom = std::tuple<NavierStokes, StaggeredFreeFlowModel>; };
+} // end namespace TTag
+
+// the fluid system
+template<class TypeTag>
+struct FluidSystem<TypeTag, TTag::SincosTest>
+{
+private:
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+public:
+ using type = FluidSystems::OnePLiquid<Scalar, Components::Constant<1, Scalar> >;
+};
+
+// Set the grid type
+template<class TypeTag>
+struct Grid<TypeTag, TTag::SincosTest> { using type = Dune::YaspGrid<2, Dune::EquidistantOffsetCoordinates<GetPropType<TypeTag, Properties::Scalar>, 2> >; };
+
+// Set the problem property
+template<class TypeTag>
+struct Problem<TypeTag, TTag::SincosTest> { using type = Dumux::SincosTestProblem<TypeTag> ; };
+
+template<class TypeTag>
+struct EnableFVGridGeometryCache<TypeTag, TTag::SincosTest> { static constexpr bool value = true; };
+template<class TypeTag>
+struct EnableGridFluxVariablesCache<TypeTag, TTag::SincosTest> { static constexpr bool value = true; };
+template<class TypeTag>
+struct EnableGridVolumeVariablesCache<TypeTag, TTag::SincosTest> { static constexpr bool value = true; };
+} // end namespace Properties
+
+/*!
+ * \ingroup NavierStokesTests
+ * \brief Test problem for the staggered grid.
+ *
+ * The 2D, incompressible Navier-Stokes equations for zero gravity and a Newtonian
+ * flow is solved and compared to an analytical solution (sums/products of trigonometric functions).
+ * For the instationary case, the velocities and pressures are periodical in time. The Dirichlet boundary conditions are
+ * consistent with the analytical solution and in the instationary case time-dependent.
+ */
+template <class TypeTag>
+class SincosTestProblem : public NavierStokesProblem<TypeTag>
+{
+ using ParentType = NavierStokesProblem<TypeTag>;
+
+ using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
+ using FVGridGeometry = GetPropType<TypeTag, Properties::FVGridGeometry>;
+ using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;
+ using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+ using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+ using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+ using TimeLoopPtr = std::shared_ptr<TimeLoop<Scalar>>;
+ using SubControlVolume = typename FVGridGeometry::SubControlVolume;
+ using FVElementGeometry = typename FVGridGeometry::LocalView;
+
+ static constexpr auto dimWorld = GetPropType<TypeTag, Properties::GridView>::dimensionworld;
+ using Element = typename FVGridGeometry::GridView::template Codim<0>::Entity;
+ using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+ using VelocityVector = Dune::FieldVector<Scalar, dimWorld>;
+
+public:
+ using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
+ using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
+
+ SincosTestProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry)
+ : ParentType(fvGridGeometry), time_(0.0), timeStepSize_(0.0)
+ {
+ isStationary_ = getParam<bool>("Problem.IsStationary");
+ enableInertiaTerms_ = getParam<bool>("Problem.EnableInertiaTerms");
+ kinematicViscosity_ = getParam<Scalar>("Component.LiquidKinematicViscosity", 1.0);
+ }
+
+ /*!
+ * \brief Returns the temperature within the domain in [K].
+ *
+ * This problem assumes a temperature of 10 degrees Celsius.
+ */
+ Scalar temperature() const
+ { return 298.0; }
+
+ /*!
+ * \brief Return the sources within the domain.
+ *
+ * \param globalPos The global position
+ */
+ NumEqVector sourceAtPos(const GlobalPosition &globalPos) const
+ {
+ NumEqVector source(0.0);
+ const Scalar x = globalPos[0];
+ const Scalar y = globalPos[1];
+ const Scalar t = time_ + timeStepSize_;
+
+ using std::cos;
+ using std::sin;
+
+ if (isStationary_)
+ {
+ source[Indices::momentumXBalanceIdx] = -2.0 * kinematicViscosity_ * cos(x) * sin(y);
+ source[Indices::momentumYBalanceIdx] = 2.0 * kinematicViscosity_ * cos(y) * sin(x);
+
+ if (!enableInertiaTerms_)
+ {
+ source[Indices::momentumXBalanceIdx] += 0.5 * sin(2.0 * x);
+ source[Indices::momentumYBalanceIdx] += 0.5 * sin(2.0 * y);
+ }
+ }
+ else
+ {
+ source[Indices::momentumXBalanceIdx] = -2.0 * cos(x) * sin(y) * (cos(2.0 * t) + sin(2.0 * t) * kinematicViscosity_);
+ source[Indices::momentumYBalanceIdx] = 2.0 * sin(x) * cos(y) * (cos(2.0 * t) + sin(2.0 * t) * kinematicViscosity_);
+ }
+
+ return source;
+ }
+
+ // \}
+ /*!
+ * \name Boundary conditions
+ */
+ // \{
+
+ /*!
+ * \brief Specifies which kind of boundary condition should be
+ * used for which equation on a given boundary control volume.
+ *
+ * \param globalPos The position of the center of the finite volume
+ */
+ BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
+ {
+ BoundaryTypes values;
+
+ // set Dirichlet values for the velocity everywhere
+ values.setDirichlet(Indices::velocityXIdx);
+ values.setDirichlet(Indices::velocityYIdx);
+
+ return values;
+ }
+
+ /*!
+ * \brief Returns whether a fixed Dirichlet value shall be used at a given cell.
+ *
+ * \param element The finite element
+ * \param fvGeometry The finite-volume geometry
+ * \param scv The sub control volume
+ * \param pvIdx The primary variable index in the solution vector
+ */
+ bool isDirichletCell(const Element& element,
+ const FVElementGeometry& fvGeometry,
+ const SubControlVolume& scv,
+ int pvIdx) const
+ {
+ // set fixed pressure in one cell
+ return (scv.dofIndex() == 0) && pvIdx == Indices::pressureIdx;
+ }
+
+ /*!
+ * \brief Returns Dirichlet boundary values at a given position.
+ *
+ * \param globalPos The global position
+ */
+ PrimaryVariables dirichletAtPos(const GlobalPosition & globalPos) const
+ {
+ // use the values of the analytical solution
+ return analyticalSolution(globalPos, time_+timeStepSize_);
+ }
+
+ /*!
+ * \brief Returns the analytical solution of the problem at a given position.
+ *
+ * \param globalPos The global position
+ * \param time The current simulation time
+ */
+ PrimaryVariables analyticalSolution(const GlobalPosition& globalPos, const Scalar time) const
+ {
+ const Scalar x = globalPos[0];
+ const Scalar y = globalPos[1];
+
+ const Scalar t = time;
+
+ PrimaryVariables values;
+
+ using std::sin;
+ using std::cos;
+
+ values[Indices::pressureIdx] = -0.25 * (cos(2.0 * x) + cos(2.0 * y));
+ values[Indices::velocityXIdx] = -1.0 * cos(x) * sin(y);
+ values[Indices::velocityYIdx] = sin(x) * cos(y);
+
+ if (!isStationary_)
+ {
+ values[Indices::pressureIdx] *= sin(2.0 * t) * sin(2.0 * t);
+ values[Indices::velocityXIdx] *= sin(2.0 * t);
+ values[Indices::velocityYIdx] *= sin(2.0 * t);
+ }
+
+ return values;
+ }
+
+ // \}
+
+ /*!
+ * \name Volume terms
+ */
+ // \{
+
+ /*!
+ * \brief Evaluates the initial value for a control volume.
+ *
+ * \param globalPos The global position
+ */
+ PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const
+ {
+ if (isStationary_)
+ {
+ PrimaryVariables values;
+ values[Indices::pressureIdx] = 0.0;
+ values[Indices::velocityXIdx] = 0.0;
+ values[Indices::velocityYIdx] = 0.0;
+
+ return values;
+ }
+ else
+ {
+ return analyticalSolution(globalPos, 0.0);
+ }
+ }
+
+ /*!
+ * \brief Updates the time
+ */
+ void updateTime(const Scalar time)
+ {
+ time_ = time;
+ }
+
+ /*!
+ * \brief Updates the time step size
+ */
+ void updateTimeStepSize(const Scalar timeStepSize)
+ {
+ timeStepSize_ = timeStepSize;
+ }
+
+private:
+ static constexpr Scalar eps_ = 1e-6;
+
+ Scalar kinematicViscosity_;
+ bool enableInertiaTerms_;
+ Scalar time_;
+ Scalar timeStepSize_;
+
+ bool isStationary_;
+};
+
+} // end namespace Dumux
+
+#endif // DUMUX_SINCOS_TEST_PROBLEM_HH
diff --git a/test/references/test_ff_navierstokes_sincos_instationary-reference.vtu b/test/references/test_ff_navierstokes_sincos_instationary-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..526f24409905ecb970f8b297c1bf10c3bfe59345
--- /dev/null
+++ b/test/references/test_ff_navierstokes_sincos_instationary-reference.vtu
@@ -0,0 +1,4233 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+ <UnstructuredGrid>
+ <Piece NumberOfCells="2500" NumberOfPoints="2601">
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diff --git a/test/references/test_ff_navierstokes_sincos_stationary-reference.vtu b/test/references/test_ff_navierstokes_sincos_stationary-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..06667d83eb7e90aa9613f49f03bd5a74f4f7c658
--- /dev/null
+++ b/test/references/test_ff_navierstokes_sincos_stationary-reference.vtu
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