diff --git a/test/freeflow/staggered/CMakeLists.txt b/test/freeflow/staggered/CMakeLists.txt
index e5afa382befaffb0b0451475ab09f3185bb52862..37f17e820269197c5fddb4427f9e2b8786ab65aa 100644
--- a/test/freeflow/staggered/CMakeLists.txt
+++ b/test/freeflow/staggered/CMakeLists.txt
@@ -79,3 +79,12 @@ dune_add_test(NAME test_navierstokes_kovasznay
--files ${CMAKE_SOURCE_DIR}/test/references/test_kovasznay-reference.vtu
${CMAKE_CURRENT_BINARY_DIR}/test_kovasznay-00002.vtu
--command "${CMAKE_CURRENT_BINARY_DIR}/test_navierstokes_kovasznay")
+
+dune_add_test(NAME test_navierstokes_angeli
+ SOURCES test_angeli.cc
+ CMAKE_GUARD HAVE_UMFPACK
+ COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+ CMD_ARGS --script fuzzy
+ --files ${CMAKE_SOURCE_DIR}/test/references/test_angeli-reference.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_angeli-00045.vtu
+ --command "${CMAKE_CURRENT_BINARY_DIR}/test_navierstokes_angeli")
diff --git a/test/freeflow/staggered/angelitestproblem.hh b/test/freeflow/staggered/angelitestproblem.hh
new file mode 100644
index 0000000000000000000000000000000000000000..3e9a8f1dec8c3e52d8968a1a37f9ec37781937c9
--- /dev/null
+++ b/test/freeflow/staggered/angelitestproblem.hh
@@ -0,0 +1,429 @@
+// -*- 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 2 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
+ *
+ * \brief Test for the instationary staggered grid Navier-Stokes model with analytical solution (Angeli et al., 2017)
+ */
+#ifndef DUMUX_ANGELI_TEST_PROBLEM_HH
+#define DUMUX_ANGELI_TEST_PROBLEM_HH
+
+#include <dumux/freeflow/staggered/problem.hh>
+#include <dumux/discretization/staggered/properties.hh>
+#include <dumux/material/components/simpleh2o.hh>
+#include <dumux/material/fluidsystems/liquidphase.hh>
+#include <dumux/material/components/constant.hh>
+
+#include <dumux/discretization/staggered/properties.hh>
+#include <dumux/freeflow/staggered/properties.hh>
+
+namespace Dumux
+{
+template <class TypeTag>
+class AngeliTestProblem;
+
+namespace Capabilities
+{
+ template<class TypeTag>
+ struct isStationary<AngeliTestProblem<TypeTag>>
+ { static const bool value = false; };
+}
+
+namespace Properties
+{
+NEW_TYPE_TAG(AngeliTestProblem, INHERITS_FROM(StaggeredModel, NavierStokes));
+
+SET_PROP(AngeliTestProblem, Fluid)
+{
+private:
+ typedef typename GET_PROP_TYPE(TypeTag, Scalar) Scalar;
+public:
+ typedef FluidSystems::LiquidPhase<Scalar, Dumux::Components::Constant<1, Scalar> > type;
+};
+
+// Set the grid type
+SET_TYPE_PROP(AngeliTestProblem, Grid, Dune::YaspGrid<2, Dune::EquidistantOffsetCoordinates<typename GET_PROP_TYPE(TypeTag, Scalar), 2> >);
+
+// Set the problem property
+SET_TYPE_PROP(AngeliTestProblem, Problem, Dumux::AngeliTestProblem<TypeTag> );
+
+SET_BOOL_PROP(AngeliTestProblem, EnableFVGridGeometryCache, true);
+
+SET_BOOL_PROP(AngeliTestProblem, EnableGlobalFluxVariablesCache, true);
+SET_BOOL_PROP(AngeliTestProblem, EnableGlobalVolumeVariablesCache, true);
+
+SET_BOOL_PROP(AngeliTestProblem, EnableInertiaTerms, true);
+}
+
+/*!
+ * \ingroup ImplicitTestProblems
+ * \brief Test problem for the staggered grid (Angeli 1947)
+ * \todo doc me!
+ */
+template <class TypeTag>
+class AngeliTestProblem : public NavierStokesProblem<TypeTag>
+{
+ using ParentType = NavierStokesProblem<TypeTag>;
+
+ using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
+ using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
+
+ // copy some indices for convenience
+ using Indices = typename GET_PROP_TYPE(TypeTag, Indices);
+ enum {
+ // Grid and world dimension
+ dim = GridView::dimension,
+ dimWorld = GridView::dimensionworld
+ };
+ enum {
+ massBalanceIdx = Indices::massBalanceIdx,
+ momentumBalanceIdx = Indices::momentumBalanceIdx,
+ momentumXBalanceIdx = Indices::momentumXBalanceIdx,
+ momentumYBalanceIdx = Indices::momentumYBalanceIdx,
+ pressureIdx = Indices::pressureIdx,
+ velocityXIdx = Indices::velocityXIdx,
+ velocityYIdx = Indices::velocityYIdx
+ };
+
+ using BoundaryTypes = typename GET_PROP_TYPE(TypeTag, BoundaryTypes);
+
+ using Element = typename GridView::template Codim<0>::Entity;
+ using Intersection = typename GridView::Intersection;
+
+ using FVElementGeometry = typename GET_PROP_TYPE(TypeTag, FVElementGeometry);
+ using SubControlVolume = typename GET_PROP_TYPE(TypeTag, SubControlVolume);
+ using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
+
+ using GlobalPosition = Dune::FieldVector<Scalar, dimWorld>;
+
+ using CellCenterPrimaryVariables = typename GET_PROP_TYPE(TypeTag, CellCenterPrimaryVariables);
+ using FacePrimaryVariables = typename GET_PROP_TYPE(TypeTag, FacePrimaryVariables);
+
+ using PrimaryVariables = typename GET_PROP_TYPE(TypeTag, PrimaryVariables);
+ using SourceValues = typename GET_PROP_TYPE(TypeTag, NumEqVector);
+ using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
+ using TimeLoopPtr = std::shared_ptr<TimeLoop<Scalar>>;
+
+ using DofTypeIndices = typename GET_PROP(TypeTag, DofTypeIndices);
+ typename DofTypeIndices::CellCenterIdx cellCenterIdx;
+ typename DofTypeIndices::FaceIdx faceIdx;
+
+public:
+ AngeliTestProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry)
+ : ParentType(fvGridGeometry), eps_(1e-6)
+ {
+ printL2Error_ = getParam<bool>("Problem.PrintL2Error");
+
+ kinematicViscosity_ = getParam<Scalar>("Component.LiquidKinematicViscosity", 1.0);
+
+ using CellArray = std::array<unsigned int, dimWorld>;
+ const auto numCells = getParam<CellArray>("Grid.Cells");
+
+ cellSizeX_ = this->fvGridGeometry().bBoxMax()[0] / numCells[0];
+ }
+
+ /*!
+ * \name Problem parameters
+ */
+ // \{
+
+ bool shouldWriteRestartFile() const
+ {
+ return false;
+ }
+
+ void postTimeStep(const SolutionVector& curSol) const
+ {
+ if(printL2Error_)
+ {
+ const auto l2error = calculateL2Error(curSol);
+ const int numCellCenterDofs = this->fvGridGeometry().gridView().size(0);
+ const int numFaceDofs = this->fvGridGeometry().gridView().size(1);
+ 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[pressureIdx] << " / " << l2error.second[pressureIdx]
+ << ", L2(vx) = " << l2error.first[velocityXIdx] << " / " << l2error.second[velocityXIdx]
+ << ", L2(vy) = " << l2error.first[velocityYIdx] << " / " << l2error.second[velocityYIdx]
+ << std::endl;
+ }
+ }
+
+ /*!
+ * \brief Return 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
+ */
+ SourceValues sourceAtPos(const GlobalPosition &globalPos) const
+ {
+ return SourceValues(0.0);
+ }
+
+ // \}
+ /*!
+ * \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(momentumBalanceIdx);
+
+ // set a fixed pressure in one cell
+ values.setDirichletCell(massBalanceIdx);
+
+ return values;
+ }
+
+ /*!
+ * \brief Return 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());
+ }
+
+ /*!
+ * \brief Return the analytical solution of the problem at a given position
+ *
+ * \param globalPos The global position
+ */
+ PrimaryVariables analyticalSolution(const GlobalPosition& globalPos, const Scalar time) const
+ {
+ Scalar x = globalPos[0];
+ Scalar y = globalPos[1];
+
+ Scalar t = time + timeLoop_->timeStepSize();
+
+ PrimaryVariables values;
+
+ values[pressureIdx] = - 0.25 * std::exp(-10.0 * kinematicViscosity_ * M_PI * M_PI * t) * M_PI * M_PI * (4.0 * std::cos(2.0 * M_PI * x) + std::cos(4.0 * M_PI * y));
+ values[velocityXIdx] = - 2.0 * M_PI * std::exp(- 5.0 * kinematicViscosity_ * M_PI * M_PI * t) * std::cos(M_PI * x) * std::sin(2.0 * M_PI * y);
+ values[velocityYIdx] = M_PI * std::exp(- 5.0 * kinematicViscosity_ * M_PI * M_PI * t) * std::sin(M_PI * x) * std::cos(2.0 * M_PI * y);
+
+ return values;
+ }
+
+ // \}
+
+ /*!
+ * \name Volume terms
+ */
+ // \{
+
+ /*!
+ * \brief Evaluate the initial value for a control volume.
+ *
+ * \param globalPos The global position
+ */
+ PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const
+ {
+ return analyticalSolution(globalPos, -timeLoop_->timeStepSize());
+ }
+
+
+ /*!
+ * \brief Calculate the L2 error between the analytical solution and the numerical approximation.
+ *
+ */
+ auto calculateL2Error(const SolutionVector& curSol) const
+ {
+ PrimaryVariables sumError(0.0), sumReference(0.0), l2NormAbs(0.0), l2NormRel(0.0);
+
+ const int numFaceDofs = this->fvGridGeometry().gridView().size(1);
+
+ std::vector<Scalar> staggeredVolume(numFaceDofs);
+ std::vector<Scalar> errorVelocity(numFaceDofs);
+ std::vector<Scalar> velocityReference(numFaceDofs);
+ std::vector<int> directionIndex(numFaceDofs);
+
+ Scalar totalVolume = 0.0;
+
+ for (const auto& element : elements(this->fvGridGeometry().gridView()))
+ {
+ auto fvGeometry = localView(this->fvGridGeometry());
+ fvGeometry.bindElement(element);
+
+ for (auto&& scv : scvs(fvGeometry))
+ {
+ // treat cell-center dofs
+ const auto dofIdxCellCenter = scv.dofIndex();
+ const auto& posCellCenter = scv.dofPosition();
+ const auto analyticalSolutionCellCenter = dirichletAtPos(posCellCenter)[cellCenterIdx];
+ const auto numericalSolutionCellCenter = curSol[cellCenterIdx][dofIdxCellCenter];
+ sumError[cellCenterIdx] += squaredDiff_(analyticalSolutionCellCenter, numericalSolutionCellCenter) * scv.volume();
+ sumReference[cellCenterIdx] += analyticalSolutionCellCenter * analyticalSolutionCellCenter * scv.volume();
+ totalVolume += scv.volume();
+
+ // treat face dofs
+ for (auto&& scvf : scvfs(fvGeometry))
+ {
+ const int dofIdxFace = scvf.dofIndex();
+ const int dirIdx = scvf.directionIndex();
+ const auto analyticalSolutionFace = dirichletAtPos(scvf.center())[faceIdx][dirIdx];
+ const auto numericalSolutionFace = curSol[faceIdx][dofIdxFace][momentumBalanceIdx];
+ directionIndex[dofIdxFace] = dirIdx;
+ errorVelocity[dofIdxFace] = squaredDiff_(analyticalSolutionFace, numericalSolutionFace);
+ velocityReference[dofIdxFace] = squaredDiff_(analyticalSolutionFace, 0.0);
+ const Scalar staggeredHalfVolume = 0.5 * scv.volume();
+ staggeredVolume[dofIdxFace] = staggeredVolume[dofIdxFace] + staggeredHalfVolume;
+ }
+ }
+ }
+
+ // get the absolute and relative discrete L2-error for cell-center dofs
+ l2NormAbs[cellCenterIdx] = std::sqrt(sumError[cellCenterIdx] / totalVolume);
+ l2NormRel[cellCenterIdx] = std::sqrt(sumError[cellCenterIdx] / sumReference[cellCenterIdx]);
+
+ // get the absolute and relative discrete L2-error for face dofs
+ for(int i = 0; i < numFaceDofs; ++i)
+ {
+ const int dirIdx = directionIndex[i];
+ const auto error = errorVelocity[i];
+ const auto ref = velocityReference[i];
+ const auto volume = staggeredVolume[i];
+ sumError[faceIdx][dirIdx] += error * volume;
+ sumReference[faceIdx][dirIdx] += ref * volume;
+ }
+
+ for(int dirIdx = 0; dirIdx < dimWorld; ++dirIdx)
+ {
+ l2NormAbs[faceIdx][dirIdx] = std::sqrt(sumError[faceIdx][dirIdx] / totalVolume);
+ l2NormRel[faceIdx][dirIdx] = std::sqrt(sumError[faceIdx][dirIdx] / sumReference[faceIdx][dirIdx]);
+ }
+ return std::make_pair(l2NormAbs, l2NormRel);
+ }
+
+ /*!
+ * \brief Returns the analytical solution for the pressure
+ */
+ auto& getAnalyticalPressureSolution() const
+ {
+ return analyticalPressure_;
+ }
+
+ /*!
+ * \brief Returns the analytical solution for the velocity
+ */
+ auto& getAnalyticalVelocitySolution() const
+ {
+ return analyticalVelocity_;
+ }
+
+ /*!
+ * \brief Returns the analytical solution for the velocity at the faces
+ */
+ auto& getAnalyticalVelocitySolutionOnFace() const
+ {
+ return analyticalVelocityOnFace_;
+ }
+
+ void setTimeLoop(TimeLoopPtr timeLoop)
+ {
+ timeLoop_ = timeLoop;
+ createAnalyticalSolution();
+ }
+
+ Scalar time() const
+ {
+ return timeLoop_->time();
+ }
+
+ /*!
+ * \brief Adds additional VTK output data to the VTKWriter. Function is called by the output module on every write.
+ */
+ void createAnalyticalSolution()
+ {
+ analyticalPressure_.resize(this->fvGridGeometry().numCellCenterDofs());
+ analyticalVelocity_.resize(this->fvGridGeometry().numCellCenterDofs());
+ analyticalVelocityOnFace_.resize(this->fvGridGeometry().numFaceDofs());
+
+ for (const auto& element : elements(this->fvGridGeometry().gridView()))
+ {
+ auto fvGeometry = localView(this->fvGridGeometry());
+ fvGeometry.bindElement(element);
+ for (auto&& scv : scvs(fvGeometry))
+ {
+ auto ccDofIdx = scv.dofIndex();
+ auto ccDofPosition = scv.dofPosition();
+ auto analyticalSolutionAtCc = 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 = analyticalSolution(faceDofPosition, time());
+ analyticalVelocityOnFace_[faceDofIdx][dirIdx] = analyticalSolutionAtFace[faceIdx][dirIdx];
+ }
+
+ analyticalPressure_[ccDofIdx] = analyticalSolutionAtCc[pressureIdx];
+ analyticalVelocity_[ccDofIdx] = analyticalSolutionAtCc[faceIdx];
+ }
+ }
+ }
+
+ private:
+
+ template<class T>
+ T squaredDiff_(const T& a, const T& b) const
+ {
+ return (a-b)*(a-b);
+ }
+
+ bool isLowerLeftCell_(const GlobalPosition& globalPos) const
+ {
+ return globalPos[0] < (this->fvGridGeometry().bBoxMin()[0] + 0.5*cellSizeX_ + eps_);
+ }
+
+ Scalar eps_;
+ Scalar cellSizeX_;
+
+ Scalar kinematicViscosity_;
+ TimeLoopPtr timeLoop_;
+ bool printL2Error_;
+ std::vector<Scalar> analyticalPressure_;
+ std::vector<GlobalPosition> analyticalVelocity_;
+ std::vector<GlobalPosition> analyticalVelocityOnFace_;
+};
+} //end namespace
+
+#endif
diff --git a/test/freeflow/staggered/test_angeli.cc b/test/freeflow/staggered/test_angeli.cc
new file mode 100644
index 0000000000000000000000000000000000000000..e786923367d4c78f4a77ca557f29bac3b7062652
--- /dev/null
+++ b/test/freeflow/staggered/test_angeli.cc
@@ -0,0 +1,270 @@
+// -*- 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 2 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
+ *
+ * \brief Test for the instationary staggered grid Navier-Stokes model with analytical solution (Angeli et al., 2017)
+ */
+ #include <config.h>
+
+ #include <ctime>
+ #include <iostream>
+
+ #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 <dune/istl/io.hh>
+
+
+#include "angelitestproblem.hh"
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/valgrind.hh>
+#include <dumux/common/dumuxmessage.hh>
+#include <dumux/common/defaultusagemessage.hh>
+
+#include <dumux/linear/seqsolverbackend.hh>
+#include <dumux/nonlinear/newtonmethod.hh>
+#include <dumux/nonlinear/newtoncontroller.hh>
+
+#include <dumux/assembly/staggeredfvassembler.hh>
+#include <dumux/assembly/diffmethod.hh>
+#include <dumux/implicit/staggered/newtoncontroller.hh>
+
+#include <dumux/discretization/methods.hh>
+
+#include <dumux/io/staggeredvtkoutputmodule.hh>
+
+/*!
+ * \brief Provides an interface for customizing error messages associated with
+ * reading in parameters.
+ *
+ * \param progName The name of the program, that was tried to be started.
+ * \param errorMsg The error message that was issued by the start function.
+ * Comprises the thing that went wrong and a general help message.
+ */
+void usage(const char *progName, const std::string &errorMsg)
+{
+ if (errorMsg.size() > 0) {
+ std::string errorMessageOut = "\nUsage: ";
+ errorMessageOut += progName;
+ errorMessageOut += " [options]\n";
+ errorMessageOut += errorMsg;
+ errorMessageOut += "\n\nThe list of mandatory arguments for this program is:\n"
+ "\t-TimeManager.TEnd End of the simulation [s] \n"
+ "\t-TimeManager.DtInitial Initial timestep size [s] \n"
+ "\t-Grid.File Name of the file containing the grid \n"
+ "\t definition in DGF format\n"
+ "\t-SpatialParams.LensLowerLeftX x-coordinate of the lower left corner of the lens [m] \n"
+ "\t-SpatialParams.LensLowerLeftY y-coordinate of the lower left corner of the lens [m] \n"
+ "\t-SpatialParams.LensUpperRightX x-coordinate of the upper right corner of the lens [m] \n"
+ "\t-SpatialParams.LensUpperRightY y-coordinate of the upper right corner of the lens [m] \n"
+ "\t-SpatialParams.Permeability Permeability of the domain [m^2] \n"
+ "\t-SpatialParams.PermeabilityLens Permeability of the lens [m^2] \n";
+
+ std::cout << errorMessageOut
+ << "\n";
+ }
+}
+
+int main(int argc, char** argv) try
+{
+ using namespace Dumux;
+
+ // define the type tag for this problem
+ using TypeTag = TTAG(AngeliTestProblem);
+
+ // 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, usage);
+
+ // try to create a grid (from the given grid file or the input file)
+ using GridCreator = typename GET_PROP_TYPE(TypeTag, GridCreator);
+ GridCreator::makeGrid();
+ GridCreator::loadBalance();
+
+ ////////////////////////////////////////////////////////////
+ // run instationary non-linear problem on this grid
+ ////////////////////////////////////////////////////////////
+
+ // we compute on the leaf grid view
+ const auto& leafGridView = GridCreator::grid().leafGridView();
+
+ // create the finite volume grid geometry
+ using FVGridGeometry = typename GET_PROP_TYPE(TypeTag, FVGridGeometry);
+ auto fvGridGeometry = std::make_shared<FVGridGeometry>(leafGridView);
+ fvGridGeometry->update();
+
+ // get some time loop parameters
+ using Scalar = typename GET_PROP_TYPE(TypeTag, Scalar);
+ const auto tEnd = getParam<Scalar>("TimeLoop.TEnd");
+ const auto maxDivisions = getParam<int>("TimeLoop.MaxTimeStepDivisions");
+ const auto maxDt = getParam<Scalar>("TimeLoop.MaxTimeStepSize");
+ auto dt = getParam<Scalar>("TimeLoop.DtInitial");
+
+ // check if we are about to restart a previously interrupted simulation
+ Scalar restartTime = 0;
+ if (Parameters::getTree().hasKey("Restart") || Parameters::getTree().hasKey("TimeLoop.Restart"))
+ restartTime = getParam<Scalar>("TimeLoop.Restart");
+
+ // instantiate time loop
+ auto timeLoop = std::make_shared<TimeLoop<Scalar>>(restartTime, dt, tEnd);
+ timeLoop->setMaxTimeStepSize(maxDt);
+
+ // the problem (initial and boundary conditions)
+ using Problem = typename GET_PROP_TYPE(TypeTag, Problem);
+ auto problem = std::make_shared<Problem>(fvGridGeometry);
+ problem->setTimeLoop(timeLoop);
+
+ // the solution vector
+ using GridView = typename GET_PROP_TYPE(TypeTag, GridView);
+ using SolutionVector = typename GET_PROP_TYPE(TypeTag, SolutionVector);
+ using DofTypeIndices = typename GET_PROP(TypeTag, DofTypeIndices);
+ typename DofTypeIndices::CellCenterIdx cellCenterIdx;
+ typename DofTypeIndices::FaceIdx faceIdx;
+ const auto numDofsCellCenter = leafGridView.size(0);
+ const auto numDofsFace = leafGridView.size(1);
+ SolutionVector x;
+ x[cellCenterIdx].resize(numDofsCellCenter);
+ x[faceIdx].resize(numDofsFace);
+ problem->applyInitialSolution(x);
+ auto xOld = x;
+
+ // the grid variables
+ using GridVariables = typename GET_PROP_TYPE(TypeTag, GridVariables);
+ auto gridVariables = std::make_shared<GridVariables>(problem, fvGridGeometry);
+ gridVariables->init(x, xOld);
+
+ // intialize the vtk output module
+ using VtkOutputFields = typename GET_PROP_TYPE(TypeTag, VtkOutputFields);
+ StaggeredVtkOutputModule<TypeTag> vtkWriter(*problem, *fvGridGeometry, *gridVariables, x, problem->name());
+ VtkOutputFields::init(vtkWriter); //! Add model specific output fields
+ vtkWriter.addField(problem->getAnalyticalPressureSolution(), "pressureExact", 1);
+ vtkWriter.addField(problem->getAnalyticalVelocitySolution(), "velocityExact", GridView::dimensionworld);
+ vtkWriter.addFaceField(problem->getAnalyticalVelocitySolutionOnFace(), "faceVelocityExact");
+ vtkWriter.write(0.0);
+
+ // the assembler with time loop for instationary problem
+ using Assembler = StaggeredFVAssembler<TypeTag, DiffMethod::numeric>;
+ auto assembler = std::make_shared<Assembler>(problem, fvGridGeometry, gridVariables, timeLoop);
+
+ // the linear solver
+ using LinearSolver = Dumux::UMFPackBackend<TypeTag>;
+ auto linearSolver = std::make_shared<LinearSolver>();
+
+ // the non-linear solver
+ using NewtonController = StaggeredNewtonController<TypeTag>;
+ using NewtonMethod = Dumux::NewtonMethod<NewtonController, Assembler, LinearSolver>;
+ auto newtonController = std::make_shared<NewtonController>(leafGridView.comm(), timeLoop);
+ NewtonMethod nonLinearSolver(newtonController, assembler, linearSolver);
+
+ // time loop
+ timeLoop->start(); do
+ {
+ // set previous solution for storage evaluations
+ assembler->setPreviousSolution(xOld);
+
+ // try solving the non-linear system
+ for (int i = 0; i < maxDivisions; ++i)
+ {
+ // linearize & solve
+ auto converged = nonLinearSolver.solve(x);
+
+ if (converged)
+ break;
+
+ if (!converged && i == maxDivisions-1)
+ DUNE_THROW(Dune::MathError,
+ "Newton solver didn't converge after "
+ << maxDivisions
+ << " time-step divisions. dt="
+ << timeLoop->timeStepSize()
+ << ".\nThe solutions of the current and the previous time steps "
+ << "have been saved to restart files.");
+ }
+
+ // make the new solution the old solution
+ xOld = x;
+ gridVariables->advanceTimeStep();
+
+ problem->createAnalyticalSolution();
+
+ // advance to the time loop to the next step
+ timeLoop->advanceTimeStep();
+
+ problem->postTimeStep(x);
+
+ // write vtk output
+ vtkWriter.write(timeLoop->time());
+
+ // report statistics of this time step
+ timeLoop->reportTimeStep();
+
+ // set new dt as suggested by newton controller
+ timeLoop->setTimeStepSize(newtonController->suggestTimeStepSize(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/staggered/test_navierstokes_angeli.input b/test/freeflow/staggered/test_navierstokes_angeli.input
new file mode 100644
index 0000000000000000000000000000000000000000..5b47d2d49e8de513126eb901b0cdeedaae050ba5
--- /dev/null
+++ b/test/freeflow/staggered/test_navierstokes_angeli.input
@@ -0,0 +1,25 @@
+[TimeLoop]
+DtInitial = 1e-12 # [s]
+TEnd = 1e-2 # [s]
+
+[Grid]
+LowerLeft = 0 0
+UpperRight = 1 1
+Cells = 50 50
+
+[Problem]
+Name = test_angeli # name passed to the output routines
+EnableGravity = false
+PrintL2Error = false
+
+[Component]
+LiquidDensity = 1
+LiquidKinematicViscosity = 0.1
+
+[ Newton ]
+MaxSteps = 10
+MaxRelativeShift = 1e-5
+
+[Vtk]
+WriteFaceData = false
+AddVelocity = true
diff --git a/test/references/test_angeli-reference.vtu b/test/references/test_angeli-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..a800d3b068c4108a703f8808c8610477aec19353
--- /dev/null
+++ b/test/references/test_angeli-reference.vtu
@@ -0,0 +1,3811 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+ <UnstructuredGrid>
+ <Piece NumberOfCells="2500" NumberOfPoints="2601">
+ <CellData Scalars="p" Vectors="velocity_component (m/s)">
+ <DataArray type="Float32" Name="p" NumberOfComponents="1" format="ascii">
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