freeflow/navierstokes/staggered/localresidual.hh

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#ifndef DUMUX_STAGGERED_NAVIERSTOKES_LOCAL_RESIDUAL_HH
#define DUMUX_STAGGERED_NAVIERSTOKES_LOCAL_RESIDUAL_HH
 
#include <dune/common/hybridutilities.hh>
 
#include <dumux/common/properties.hh>
#include <dumux/discretization/method.hh>
#include <dumux/discretization/extrusion.hh>
#include <dumux/assembly/staggeredlocalresidual.hh>
#include <dumux/freeflow/nonisothermal/localresidual.hh>
 
namespace Dumux {
 
namespace Impl {
template<class T>
static constexpr bool isRotationalExtrusion = false;
 
template<int radialAxis>
static constexpr bool isRotationalExtrusion<RotationalExtrusion<radialAxis>> = true;
} // end namespace Impl
 
// forward declaration
template<class TypeTag, class DiscretizationMethod>
class NavierStokesResidualImpl;
 
template<class TypeTag>
class NavierStokesResidualImpl<TypeTag, DiscretizationMethods::Staggered>
: public StaggeredLocalResidual<TypeTag>
{
    using ParentType = StaggeredLocalResidual<TypeTag>;
    friend class StaggeredLocalResidual<TypeTag>;
 
    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
 
    using GridVolumeVariables = typename GridVariables::GridVolumeVariables;
    using ElementVolumeVariables = typename GridVolumeVariables::LocalView;
    using VolumeVariables = typename GridVolumeVariables::VolumeVariables;
 
    using GridFluxVariablesCache = typename GridVariables::GridFluxVariablesCache;
    using ElementFluxVariablesCache = typename GridFluxVariablesCache::LocalView;
 
    using GridFaceVariables = typename GridVariables::GridFaceVariables;
    using ElementFaceVariables = typename GridFaceVariables::LocalView;
 
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Implementation = GetPropType<TypeTag, Properties::LocalResidual>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using GridView = typename GridGeometry::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;
    using Extrusion = Extrusion_t<GridGeometry>;
    using ElementBoundaryTypes = GetPropType<TypeTag, Properties::ElementBoundaryTypes>;
    using CellCenterPrimaryVariables = GetPropType<TypeTag, Properties::CellCenterPrimaryVariables>;
    using FacePrimaryVariables = GetPropType<TypeTag, Properties::FacePrimaryVariables>;
    using FluxVariables = GetPropType<TypeTag, Properties::FluxVariables>;
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
 
    static constexpr bool normalizePressure = getPropValue<TypeTag, Properties::NormalizePressure>();
 
    using CellCenterResidual = CellCenterPrimaryVariables;
    using FaceResidual = FacePrimaryVariables;
 
    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
 
public:
    using EnergyLocalResidual = FreeFlowEnergyLocalResidual<GridGeometry, FluxVariables, ModelTraits::enableEnergyBalance(), (ModelTraits::numFluidComponents() > 1)>;
 
    // account for the offset of the cell center privars within the PrimaryVariables container
    static constexpr auto cellCenterOffset = ModelTraits::numEq() - CellCenterPrimaryVariables::dimension;
    static_assert(cellCenterOffset == ModelTraits::dim(), "cellCenterOffset must equal dim for staggered NavierStokes");
 
    using ParentType::ParentType;
 
    CellCenterPrimaryVariables computeFluxForCellCenter(const Problem& problem,
                                                        const Element &element,
                                                        const FVElementGeometry& fvGeometry,
                                                        const ElementVolumeVariables& elemVolVars,
                                                        const ElementFaceVariables& elemFaceVars,
                                                        const SubControlVolumeFace &scvf,
                                                        const ElementFluxVariablesCache& elemFluxVarsCache) const
    {
        FluxVariables fluxVars;
        CellCenterPrimaryVariables flux = fluxVars.computeMassFlux(problem, element, fvGeometry, elemVolVars,
                                                                   elemFaceVars, scvf, elemFluxVarsCache[scvf]);
 
        EnergyLocalResidual::heatFlux(flux, problem, element, fvGeometry, elemVolVars, elemFaceVars, scvf);
 
        return flux;
    }
 
    CellCenterPrimaryVariables computeSourceForCellCenter(const Problem& problem,
                                                          const Element &element,
                                                          const FVElementGeometry& fvGeometry,
                                                          const ElementVolumeVariables& elemVolVars,
                                                          const ElementFaceVariables& elemFaceVars,
                                                          const SubControlVolume &scv) const
    {
        CellCenterPrimaryVariables result(0.0);
 
        // get the values from the problem
        const auto sourceValues = problem.source(element, fvGeometry, elemVolVars, elemFaceVars, scv);
 
        // copy the respective cell center related values to the result
        for (int i = 0; i < result.size(); ++i)
            result[i] = sourceValues[i + cellCenterOffset];
 
        return result;
    }
 
 
    CellCenterPrimaryVariables computeStorageForCellCenter(const Problem& problem,
                                                           const SubControlVolume& scv,
                                                           const VolumeVariables& volVars) const
    {
        CellCenterPrimaryVariables storage;
        storage[Indices::conti0EqIdx - ModelTraits::dim()] = volVars.density();
 
        EnergyLocalResidual::fluidPhaseStorage(storage, volVars);
 
        return storage;
    }
 
    FacePrimaryVariables computeStorageForFace(const Problem& problem,
                                               const SubControlVolumeFace& scvf,
                                               const VolumeVariables& volVars,
                                               const ElementFaceVariables& elemFaceVars) const
    {
        FacePrimaryVariables storage(0.0);
        const Scalar velocity = elemFaceVars[scvf].velocitySelf();
        storage[0] = volVars.density() * velocity;
        return storage;
    }
 
    FacePrimaryVariables computeSourceForFace(const Problem& problem,
                                              const Element& element,
                                              const FVElementGeometry& fvGeometry,
                                              const SubControlVolumeFace& scvf,
                                              const ElementVolumeVariables& elemVolVars,
                                              const ElementFaceVariables& elemFaceVars) const
    {
        FacePrimaryVariables source(0.0);
        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];
        source += problem.gravity()[scvf.directionIndex()] * insideVolVars.density();
        source += problem.source(element, fvGeometry, elemVolVars, elemFaceVars, scvf)[Indices::velocity(scvf.directionIndex())];
 
        // Axisymmetric problems in 2D feature an extra source terms arising from the transformation to cylindrical coordinates.
        // See Ferziger/Peric: Computational methods for fluid dynamics chapter 8.
        // https://doi.org/10.1007/978-3-540-68228-8 (page 301)
        if constexpr (ModelTraits::dim() == 2 && Impl::isRotationalExtrusion<Extrusion>)
        {
            if (scvf.directionIndex() == Extrusion::radialAxis)
            {
                // Velocity term
                const auto r = scvf.center()[scvf.directionIndex()];
                source -= -2.0*insideVolVars.effectiveViscosity() * elemFaceVars[scvf].velocitySelf() / (r*r);
 
                // Pressure term (needed because we incorporate pressure in terms of a surface integral).
                // grad(p) becomes div(pI) + (p/r)*n_r in cylindrical coordinates. The second term
                // is new with respect to Cartesian coordinates and handled below as a source term.
                const Scalar pressure =
                    normalizePressure ? insideVolVars.pressure() - problem.initial(scvf)[Indices::pressureIdx]
                                      : insideVolVars.pressure();
 
                source += pressure/r;
            }
        }
 
        return source;
    }
 
    FacePrimaryVariables computeFluxForFace(const Problem& problem,
                                            const Element& element,
                                            const SubControlVolumeFace& scvf,
                                            const FVElementGeometry& fvGeometry,
                                            const ElementVolumeVariables& elemVolVars,
                                            const ElementFaceVariables& elemFaceVars,
                                            const ElementFluxVariablesCache& elemFluxVarsCache) const
    {
        FluxVariables fluxVars;
        return fluxVars.computeMomentumFlux(problem, element, scvf, fvGeometry, elemVolVars, elemFaceVars, elemFluxVarsCache.gridFluxVarsCache());
    }
 
    CellCenterResidual computeBoundaryFluxForCellCenter(const Problem& problem,
                                                        const Element& element,
                                                        const FVElementGeometry& fvGeometry,
                                                        const SubControlVolumeFace& scvf,
                                                        const ElementVolumeVariables& elemVolVars,
                                                        const ElementFaceVariables& elemFaceVars,
                                                        const ElementBoundaryTypes& elemBcTypes,
                                                        const ElementFluxVariablesCache& elemFluxVarsCache) const
    {
        CellCenterResidual result(0.0);
 
        if (scvf.boundary())
        {
            const auto bcTypes = problem.boundaryTypes(element, scvf);
 
            // no fluxes occur over symmetry boundaries
            if (bcTypes.isSymmetry())
                return result;
 
            // treat Dirichlet and outflow BCs
            result = computeFluxForCellCenter(problem, element, fvGeometry, elemVolVars, elemFaceVars, scvf, elemFluxVarsCache);
 
            // treat Neumann BCs, i.e. overwrite certain fluxes by user-specified values
            static constexpr auto numEqCellCenter = CellCenterResidual::dimension;
            if (bcTypes.hasNeumann())
            {
                const auto extrusionFactor = elemVolVars[scvf.insideScvIdx()].extrusionFactor();
                const auto neumannFluxes = problem.neumann(element, fvGeometry, elemVolVars, elemFaceVars, scvf);
 
                for (int eqIdx = 0; eqIdx < numEqCellCenter; ++eqIdx)
                {
                    if (bcTypes.isNeumann(eqIdx + cellCenterOffset))
                        result[eqIdx] = neumannFluxes[eqIdx + cellCenterOffset] * extrusionFactor * Extrusion::area(fvGeometry, scvf);
                }
            }
 
            // account for wall functions, if used
            incorporateWallFunction_(result, problem, element, fvGeometry, scvf, elemVolVars, elemFaceVars);
        }
        return result;
    }
 
    void evalDirichletBoundariesForFace(FaceResidual& residual,
                                        const Problem& problem,
                                        const Element& element,
                                        const FVElementGeometry& fvGeometry,
                                        const SubControlVolumeFace& scvf,
                                        const ElementVolumeVariables& elemVolVars,
                                        const ElementFaceVariables& elemFaceVars,
                                        const ElementBoundaryTypes& elemBcTypes,
                                        const ElementFluxVariablesCache& elemFluxVarsCache) const
    {
        if (scvf.boundary())
        {
            // handle the actual boundary conditions:
            const auto bcTypes = problem.boundaryTypes(element, scvf);
 
            if(bcTypes.isDirichlet(Indices::velocity(scvf.directionIndex())))
            {
                // set a fixed value for the velocity for Dirichlet boundary conditions
                const Scalar velocity = elemFaceVars[scvf].velocitySelf();
                const Scalar dirichletValue = problem.dirichlet(element, scvf)[Indices::velocity(scvf.directionIndex())];
                residual = velocity - dirichletValue;
            }
            else if(bcTypes.isSymmetry())
            {
                // for symmetry boundary conditions, there is no flow across the boundary and
                // we therefore treat it like a Dirichlet boundary conditions with zero velocity
                const Scalar velocity = elemFaceVars[scvf].velocitySelf();
                const Scalar fixedValue = 0.0;
                residual = velocity - fixedValue;
            }
        }
    }
 
    FaceResidual computeBoundaryFluxForFace(const Problem& problem,
                                            const Element& element,
                                            const FVElementGeometry& fvGeometry,
                                            const SubControlVolumeFace& scvf,
                                            const ElementVolumeVariables& elemVolVars,
                                            const ElementFaceVariables& elemFaceVars,
                                            const ElementBoundaryTypes& elemBcTypes,
                                            const ElementFluxVariablesCache& elemFluxVarsCache) const
    {
        FaceResidual result(0.0);
 
        if (scvf.boundary())
        {
            FluxVariables fluxVars;
 
            // handle the actual boundary conditions:
            const auto bcTypes = problem.boundaryTypes(element, scvf);
            if (bcTypes.isNeumann(Indices::velocity(scvf.directionIndex())))
            {
                // the source term has already been accounted for, here we
                // add a given Neumann flux for the face on the boundary itself ...
                const auto extrusionFactor = elemVolVars[scvf.insideScvIdx()].extrusionFactor();
                result = problem.neumann(element, fvGeometry, elemVolVars, elemFaceVars, scvf)[Indices::velocity(scvf.directionIndex())]
                                         * extrusionFactor * Extrusion::area(fvGeometry, scvf);
 
                // ... and treat the fluxes of the remaining (frontal and lateral) faces of the staggered control volume
                result += fluxVars.computeMomentumFlux(problem, element, scvf, fvGeometry, elemVolVars, elemFaceVars, elemFluxVarsCache.gridFluxVarsCache());
            }
            else if(bcTypes.isDirichlet(Indices::pressureIdx))
            {
                // we are at an "fixed pressure" boundary for which the resdiual of the momentum balance needs to be assembled
                // as if it where inside the domain and not on the boundary (source term has already been acounted for)
                result = fluxVars.computeMomentumFlux(problem, element, scvf, fvGeometry, elemVolVars, elemFaceVars, elemFluxVarsCache.gridFluxVarsCache());
 
                // incorporate the inflow or outflow contribution
                result += fluxVars.inflowOutflowBoundaryFlux(problem, scvf, fvGeometry, elemVolVars, elemFaceVars);
            }
        }
        return result;
    }
 
private:
 
    template<class ...Args, bool turbulenceModel = ModelTraits::usesTurbulenceModel(), std::enable_if_t<!turbulenceModel, int> = 0>
    void incorporateWallFunction_(Args&&... args) const
    {}
 
    template<bool turbulenceModel = ModelTraits::usesTurbulenceModel(), std::enable_if_t<turbulenceModel, int> = 0>
    void incorporateWallFunction_(CellCenterResidual& boundaryFlux,
                                  const Problem& problem,
                                  const Element& element,
                                  const FVElementGeometry& fvGeometry,
                                  const SubControlVolumeFace& scvf,
                                  const ElementVolumeVariables& elemVolVars,
                                  const ElementFaceVariables& elemFaceVars) const
    {
        static constexpr auto numEqCellCenter = CellCenterResidual::dimension;
        const auto extrusionFactor = elemVolVars[scvf.insideScvIdx()].extrusionFactor();
 
        // account for wall functions, if used
        for(int eqIdx = 0; eqIdx < numEqCellCenter; ++eqIdx)
        {
            // use a wall function
            if(problem.useWallFunction(element, scvf, eqIdx + cellCenterOffset))
            {
                boundaryFlux[eqIdx] = problem.wallFunction(element, fvGeometry, elemVolVars, elemFaceVars, scvf)[eqIdx]
                                                           * extrusionFactor * Extrusion::area(fvGeometry, scvf);
            }
        }
    }
 
    Implementation &asImp_()
    { return *static_cast<Implementation *>(this); }
 
    const Implementation &asImp_() const
    { return *static_cast<const Implementation *>(this); }
};
 
} // end namespace Dumux
 
#endif