[test][shallowwater] Add bowl test for new upwind mobility

test/freeflow/shallowwater/CMakeLists.txt

+add_subdirectory(bowl)
 add_subdirectory(dambreak)
 add_subdirectory(roughchannel)

test/freeflow/shallowwater/bowl/CMakeLists.txt

+dune_symlink_to_source_files(FILES "params.input")
+
+dumux_add_test(NAME test_shallowwater_bowl
+              SOURCES main.cc
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS       --script fuzzy
+                             --files ${CMAKE_SOURCE_DIR}/test/references/test_ff_shallowwater_bowl-reference.vtu
+                                     ${CMAKE_CURRENT_BINARY_DIR}/bowl-00001.vtu
+                             --zeroThreshold {"velocityY":1e-14}
+                             --command "${CMAKE_CURRENT_BINARY_DIR}/test_shallowwater_bowl params.input
+                             -Problem.Name bowl")

test/freeflow/shallowwater/bowl/main.cc

+// -*- 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
+ * \ingroup ShallowWaterTests
+ * \brief A test for the shallow water model (bowl).
+ */
+#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 <dumux/io/vtkoutputmodule.hh>
+
+#include <dumux/common/properties.hh>
+#include <dumux/common/parameters.hh>
+#include <dumux/common/dumuxmessage.hh>
+
+#include <dumux/io/grid/gridmanager.hh>
+#include <dumux/linear/amgbackend.hh>
+#include <dumux/nonlinear/newtonsolver.hh>
+
+#include <dumux/assembly/fvassembler.hh>
+
+#include "problem.hh"
+
+////////////////////////
+// the main function
+////////////////////////
+int main(int argc, char** argv) try
+{
+    using namespace Dumux;
+
+    // define the type tag for this problem
+    using TypeTag = Properties::TTag::Bowl;
+
+    // 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 GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+    auto gridGeometry = std::make_shared<GridGeometry>(leafGridView);
+    gridGeometry->update();
+
+    // the problem (initial and boundary conditions)
+    using Problem = GetPropType<TypeTag, Properties::Problem>;
+    auto problem = std::make_shared<Problem>(gridGeometry);
+
+    // the solution vector
+    using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+    SolutionVector x(gridGeometry->numDofs());
+    problem->applyInitialSolution(x);
+    auto xOld = x;
+
+    // the grid variables
+    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+    auto gridVariables = std::make_shared<GridVariables>(problem, gridGeometry);
+    gridVariables->init(x);
+
+    // 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");
+
+    // intialize the vtk output module
+    using IOFields = GetPropType<TypeTag, Properties::IOFields>;
+
+    VtkOutputModule<GridVariables, SolutionVector> vtkWriter(*gridVariables,x, problem->name());
+    vtkWriter.addField(problem->getExactWaterDepth(), "exactWaterDepth");
+    problem->updateAnalyticalSolution(0.0);
+    IOFields::initOutputModule(vtkWriter);
+    vtkWriter.write(0.0);
+
+    // instantiate time loop
+    auto timeLoop = std::make_shared<CheckPointTimeLoop<Scalar>>(0, dt, tEnd);
+    timeLoop->setMaxTimeStepSize(maxDt);
+
+    // the assembler with time loop for instationary problem
+    using Assembler = FVAssembler<TypeTag, DiffMethod::numeric>;
+    auto assembler = std::make_shared<Assembler>(problem, gridGeometry, gridVariables, timeLoop, xOld);
+
+    // the linear solver
+    using LinearSolver = AMGBiCGSTABBackend<LinearSolverTraits<GridGeometry>>;
+    auto linearSolver = std::make_shared<LinearSolver>(leafGridView, gridGeometry->dofMapper());
+
+    // the non-linear solver
+    using NewtonSolver = Dumux::NewtonSolver<Assembler, LinearSolver>;
+    NewtonSolver nonLinearSolver(assembler, linearSolver);
+
+    //! set some check point at the end of the time loop
+    timeLoop->setCheckPoint(tEnd);
+
+    //! Compute L2 error for the initial solution (should be zero)
+    problem->computeL2error(timeLoop->time(), x, *gridVariables);
+
+    // time loop
+    timeLoop->start(); do
+    {
+        nonLinearSolver.solve(x,*timeLoop);
+
+        // make the new solution the old solution
+        xOld = x;
+        gridVariables->advanceTimeStep();
+
+        // update the analytical solution
+        problem->updateAnalyticalSolution(timeLoop->time());
+        problem->computeL2error(timeLoop->time(), x, *gridVariables);
+
+        // advance to the time loop to the next step
+        timeLoop->advanceTimeStep();
+
+        // write vtk output
+        if (timeLoop->isCheckPoint())
+            vtkWriter.write(timeLoop->time());
+
+        // report statistics of this time step
+        timeLoop->reportTimeStep();
+
+        // set new dt as suggested by newton controller
+        timeLoop->setTimeStepSize(nonLinearSolver.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;
+}
+
+catch (const Dumux::ParameterException &e)
+{
+    std::cerr << std::endl << e << " ---> Abort!" << std::endl;
+    return 1;
+}
+catch (const 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 (const 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;
+}

test/freeflow/shallowwater/bowl/params.input

+[Problem]
+Name = bowl
+BowlDepthAtCenter = 0.03 # [m]
+BowlParaboloidRadius = 1.6 # [m]
+BowlInitialWaterElevationAtCenter = 0.005 # [m]
+Gravity = 9.81 # [m/s^2]
+
+[FluxLimiterLET]
+UpperWaterDepth = 1.0E-5
+LowerWaterDepth = 1.0E-7
+UpwindFluxLimiting = true
+
+[TimeLoop]
+TEnd = 13.104 # [s] 6.552 is one period
+MaxTimeStepSize = 0.1 # [s]
+DtInitial = 0.01 # [s]
+
+[Grid]
+Positions0 = -2.0 2.0
+Positions1 = -2.0 2.0
+Cells0 = 50
+Cells1 = 50
+
+[Newton]
+EnableAbsoluteResidualCriterion = true
+MaxAbsoluteResidual = 1e-6
+RetryTimeStepReductionFactor = 0.5
+SatisfyResidualAndShiftCriterion = "false"
+EnableDynamicOutput = false
+EnablePartialReassembly = false
+TargetSteps = 6
+MaxSteps = 10
+UseLineSearch = true
+
+[LinearSolver]
+MaxIterations = 200
+ResidualReduction = 1e-5
+
+

test/freeflow/shallowwater/bowl/problem.hh

+// -*- 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
+ * \ingroup ShallowWaterTests
+ * \brief A test for the Shallow water model (bowl).
+ */
+#ifndef DUMUX_BOWL_TEST_PROBLEM_HH
+#define DUMUX_BOWL_TEST_PROBLEM_HH
+
+#include <dune/grid/yaspgrid.hh>
+#include <dumux/discretization/cctpfa.hh>
+#include "spatialparams.hh"
+#include <dumux/common/parameters.hh>
+
+#include <dumux/freeflow/shallowwater/model.hh>
+#include <dumux/freeflow/shallowwater/problem.hh>
+#include <dumux/freeflow/shallowwater/boundaryfluxes.hh>
+
+namespace Dumux {
+
+template <class TypeTag>
+class BowlProblem;
+
+// Specify the properties for the problem
+namespace Properties {
+
+// Create new type tags
+namespace TTag {
+struct Bowl { using InheritsFrom = std::tuple<ShallowWater, CCTpfaModel>; };
+} // end namespace TTag
+
+template<class TypeTag>
+struct Grid<TypeTag, TTag::Bowl>
+{ using type = Dune::YaspGrid<2, Dune::TensorProductCoordinates<GetPropType<TypeTag, Properties::Scalar>, 2> >; };
+
+// Set the problem property
+template<class TypeTag>
+struct Problem<TypeTag, TTag::Bowl>
+{ using type = Dumux::BowlProblem<TypeTag>; };
+
+// Set the spatial parameters
+template<class TypeTag>
+struct SpatialParams<TypeTag, TTag::Bowl>
+{
+private:
+    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
+    using VolumeVariables = typename ElementVolumeVariables::VolumeVariables;
+public:
+    using type = BowlSpatialParams<GridGeometry, Scalar, VolumeVariables>;
+};
+
+template<class TypeTag>
+struct EnableGridGeometryCache<TypeTag, TTag::Bowl>
+{ static constexpr bool value = true; };
+
+template<class TypeTag>
+struct EnableGridVolumeVariablesCache<TypeTag, TTag::Bowl>
+{ static constexpr bool value = false; };
+} // end namespace Properties
+
+/*!
+ * \ingroup ShallowWaterTests
+ * \brief A wetting and drying test with sloshing water in a bowl.
+ *
+ * The domain is 4 meters long and 4 meters wide. The center of the domain is loacted at
+ * x = 0 and y = 0. There is no flow over the boundaries and no friction is considered.
+ *
+ * This example is demanding for the implicit model if a high mesh resolution is applied
+ * (e.g. 150x150 cells) in combination with a large time step size. Using the new limiting
+ * (UpwindFluxLimiting = true) will help to improve the convergence for such cases.
+ *
+ * This test uses a low mesh resoultion and only ensures that UpwindFluxLimiting for the mobility
+ * works.
+ *
+ * The results are checked against a analytical solution which is based on the "Thacker-Solution"
+ * (William Thacker, "Some exact solutions to the nonlinear shallow-water wave equations", Journal
+ * of Fluid Mechanics, 107:499–508, 1981). Further examples and details on the solution are given
+ * in SWASHES (Shallow Water Analytic Solutions for Hydraulic and Environmental Studies,
+ * https://www.idpoisson.fr/swashes/).
+ *
+ * This problem uses the \ref ShallowWaterModel
+ */
+template <class TypeTag>
+class BowlProblem : public ShallowWaterProblem<TypeTag>
+{
+    using ParentType = ShallowWaterProblem<TypeTag>;
+    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
+    using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
+    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
+    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
+    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
+    using NeumannFluxes = GetPropType<TypeTag, Properties::NumEqVector>;
+    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
+    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
+    using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView;
+    using VolumeVariables = typename ElementVolumeVariables::VolumeVariables;
+    using FVElementGeometry = typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView;
+    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
+    using GridView = GetPropType<TypeTag, Properties::GridView>;
+    using Element = typename GridView::template Codim<0>::Entity;
+    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
+    using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;
+    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
+    using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
+
+public:
+    BowlProblem(std::shared_ptr<const GridGeometry> gridGeometry)
+    : ParentType(gridGeometry)
+    {
+        using std::sqrt;
+        using std::pow;
+
+        name_ = getParam<std::string>("Problem.Name");
+        gravity_ = getParam<Scalar>("Problem.Gravity");
+        bowlDepthAtCenter_ =  getParam<Scalar>("Problem.BowlDepthAtCenter");
+        bowlParaboloidRadius_ =  getParam<Scalar>("Problem.BowlParaboloidRadius");
+        bowlInitialWaterElevationAtCenter_ =  getParam<Scalar>("Problem.BowlInitialWaterElevationAtCenter");
+        bowlAnalyticParameterOmega_ = sqrt(8.0 * gravity_ * bowlDepthAtCenter_) / bowlParaboloidRadius_;
+        bowlAnalyticParameterA_ = (pow(bowlDepthAtCenter_ + bowlInitialWaterElevationAtCenter_, 2.0) -
+                                  pow(bowlDepthAtCenter_, 2.0)) /
+                                  (pow(bowlDepthAtCenter_ + bowlInitialWaterElevationAtCenter_, 2.0)+
+                                  pow(bowlDepthAtCenter_, 2.0));
+        exactWaterDepth_.resize(gridGeometry->numDofs(), 0.0);
+        updateAnalyticalSolution(0.0);
+    }
+
+    //! Get the analytical water depth
+    const std::vector<Scalar>& getExactWaterDepth()
+    {
+        return exactWaterDepth_;
+    }
+
+    //! Get the analctic water depth at
+    Scalar calculateAnalyticWaterDepth(Scalar time, Scalar x, Scalar y)
+    {
+        using std::max;
+        using std::sqrt;
+        using std::pow;
+        using std::cos;
+
+        auto waterDepth = max(bowlDepthAtCenter_* ((sqrt(1.0 - pow(bowlAnalyticParameterA_, 2.0)))/
+                          (1.0 - bowlAnalyticParameterA_ * cos(bowlAnalyticParameterOmega_ * time))-
+                          1.0 - (pow(x, 2.0) + pow(y, 2.0)) / pow(bowlParaboloidRadius_, 2.0) *
+                          ((1.0- pow(bowlAnalyticParameterA_, 2.0)) /
+                          (pow(1.0 - bowlAnalyticParameterA_ *
+                          cos(bowlAnalyticParameterOmega_ * time), 2.0)) - 1.0)) -
+                          bowlDepthAtCenter_ *((pow(x, 2.0) + pow(y, 2.0))/
+                          pow(bowlParaboloidRadius_, 2.0) - 1.0), 1.0E-5);
+
+        return waterDepth;
+    }
+
+    //! Compute L2 error
+    void computeL2error(const Scalar time,
+                        const SolutionVector& curSol,
+                        const GridVariables& gridVariables)
+    {
+        Scalar l2error = 0.0;
+
+        //first ensure that the Analytical solution is up-to-date
+        updateAnalyticalSolution(time);
+
+        for (const auto& element : elements(this->gridGeometry().gridView()))
+        {
+            const auto eIdx = this->gridGeometry().elementMapper().index(element);
+            const auto& globalPos = element.geometry().center();
+            auto fvGeometry = localView(this->gridGeometry());
+            fvGeometry.bindElement(element);
+            auto elemVolVars = localView(gridVariables.curGridVolVars());
+            elemVolVars.bindElement(element, fvGeometry, curSol);
+            exactWaterDepth_[eIdx] = calculateAnalyticWaterDepth(time, globalPos[0], globalPos[1]);
+
+            for (auto&& scv : scvs(fvGeometry))
+            {
+                using std::pow;
+                l2error += pow(exactWaterDepth_[eIdx] - elemVolVars[scv].waterDepth(), 2.0);
+            }
+        }
+        using std::sqrt;
+        l2error = sqrt(l2error);
+        l2error = this->gridGeometry().gridView().comm().sum(l2error);
+
+        if (this->gridGeometry().gridView().comm().rank() == 0)
+        {
+            std::cout << "L2 error at t =  "
+                  <<  time << " seconds "
+                  << " for "
+                  << std::setw(6) << this->gridGeometry().gridView().size(0)
+                  << " elements: "
+                  << std::scientific
+                  << l2error
+                  << std::endl;
+        }
+    }
+
+    //! Udpate the analytical solution
+    void updateAnalyticalSolution(const Scalar time)
+    {
+        for (const auto& element : elements(this->gridGeometry().gridView()))
+        {
+            const auto eIdx = this->gridGeometry().elementMapper().index(element);
+            const auto& globalPos = element.geometry().center();
+
+            exactWaterDepth_[eIdx] = calculateAnalyticWaterDepth(time, globalPos[0], globalPos[1]);
+        }
+    }
+
+    /*!
+     * \name Problem parameters
+     */
+    // \{
+
+    /*!
+     * \brief The problem name
+     *
+     * This is used as a prefix for files generated by the simulation.
+     */
+    const std::string& name() const
+    {
+        return name_;
+    }
+
+     /*!
+     * \brief Evaluate the source term for all balance equations within a given
+     *        sub-control-volume.
+     *
+     * This is the method for the case where the source term is
+     * potentially solution dependent and requires some quantities that
+     * are specific to the fully-implicit method.
+     *
+     * \param element The finite element
+     * \param fvGeometry The finite-volume geometry
+     * \param elemVolVars All volume variables for the element
+     * \param scv The sub control volume
+     *
+     * For this method, the \a values parameter stores the conserved quantity rate
+     * generated or annihilate per volume unit. Positive values mean
+     * that the conserved quantity is created, negative ones mean that it vanishes.
+     * E.g. for the mass balance that would be a mass rate in \f$ [ kg / (m^3 \cdot s)] \f$.
+     */
+     NumEqVector source(const Element& element,
+                        const FVElementGeometry& fvGeometry,
+                        const ElementVolumeVariables& elemVolVars,
+                        const SubControlVolume &scv) const
+    {
+        NumEqVector source (0.0);
+
+        return source;
+    }
+
+    // \}
+
+    /*!
+     * \name Boundary conditions
+     */
+    // \{
+
+    /*!
+     * \brief Specifies which kind of boundary condition should be
+     *        used for which equation on a given boundary segment.
+     *
+     * \param globalPos The position for which the boundary type is set
+     */
+    BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
+    {
+        BoundaryTypes bcTypes;
+        bcTypes.setAllNeumann();
+        return bcTypes;
+    }
+
+    /*!
+     * \brief Specifies the neumann boundary
+     *
+     *  We need the Riemann invariants to compute the values depending of the boundary type.
+     *  Since we use a weak imposition we do not have a dirichlet value. We impose fluxes
+     *  based on q, h, etc. computed with the Riemann invariants
+     *
+     * \param element
+     * \param fvGeometry
+     * \param elemVolVars
+     * \param scvf
+     */
+    NeumannFluxes neumann(const Element& element,
+                          const FVElementGeometry& fvGeometry,
+                          const ElementVolumeVariables& elemVolVars,
+                          const ElementFluxVariablesCache& elemFluxVarsCache,
+                          const SubControlVolumeFace& scvf) const
+    {
+        NeumannFluxes values(0.0);
+
+        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
+        const auto& insideVolVars = elemVolVars[insideScv];
+        const auto& nxy = scvf.unitOuterNormal();
+        const auto gravity = this->spatialParams().gravity(scvf.center());
+        std::array<Scalar, 3> boundaryStateVariables;
+
+        //no flow with zero normal velocity and tangential velocity
+        const auto vNormalGhost = -(nxy[0] * insideVolVars.velocity(0) +  nxy[1] * insideVolVars.velocity(1));
+        const auto vTangentialGhost = -nxy[1] * insideVolVars.velocity(0) + nxy[0] * insideVolVars.velocity(1);
+
+        boundaryStateVariables[0] = insideVolVars.waterDepth();
+        boundaryStateVariables[1] =  nxy[0] * vNormalGhost - nxy[1] * vTangentialGhost;
+        boundaryStateVariables[2] =  nxy[1] * vNormalGhost + nxy[0] * vTangentialGhost;
+
+        auto riemannFlux = ShallowWater::riemannProblem(insideVolVars.waterDepth(),
+                                                        boundaryStateVariables[0],
+                                                        insideVolVars.velocity(0),
+                                                        boundaryStateVariables[1],
+                                                        insideVolVars.velocity(1),
+                                                        boundaryStateVariables[2],
+                                                        insideVolVars.bedSurface(),
+                                                        insideVolVars.bedSurface(),
+                                                        gravity,
+                                                        nxy);
+
+        values[Indices::massBalanceIdx] = riemannFlux[0];
+        values[Indices::velocityXIdx]   = riemannFlux[1];
+        values[Indices::velocityYIdx]   = riemannFlux[2];
+
+        return values;
+    }