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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-

// vi: set et ts=4 sw=4 sts=4:

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#ifndef DUMUX_NAVIERSTOKES_STAGGERED_FLUXVARIABLES_HH

#define DUMUX_NAVIERSTOKES_STAGGERED_FLUXVARIABLES_HH


#include <array>

#include <optional>

#include <type_traits>


#include <dumux/common/math.hh>

#include <dumux/common/exceptions.hh>

#include <dumux/common/parameters.hh>

#include <dumux/common/properties.hh>

#include <dumux/common/typetraits/problem.hh>


#include <dumux/flux/fluxvariablesbase.hh>

#include <dumux/discretization/method.hh>

#include <dumux/discretization/extrusion.hh>


#include "staggeredupwindhelper.hh"

#include "velocitygradients.hh"


namespace Dumux {


// forward declaration

template<class TypeTag, class DiscretizationMethod>

class NavierStokesFluxVariablesImpl;


template<class TypeTag>

class NavierStokesFluxVariablesImpl<TypeTag, DiscretizationMethods::Staggered>

: public FluxVariablesBase<GetPropType<TypeTag, Properties::Problem>,

                           typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView,

                           typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView,

                           typename GetPropType<TypeTag, Properties::GridFluxVariablesCache>::LocalView>

{

    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 FluxVariablesCache = typename GridFluxVariablesCache::FluxVariablesCache;


    using GridFaceVariables = typename GridVariables::GridFaceVariables;

    using ElementFaceVariables = typename GridFaceVariables::LocalView;

    using FaceVariables = typename GridFaceVariables::FaceVariables;


    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 Scalar = GetPropType<TypeTag, Properties::Scalar>;

    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;

    using Indices = typename ModelTraits::Indices;

    using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace;

    using FaceFrontalSubControlVolumeFace = typename GridGeometry::Traits::FaceFrontalSubControlVolumeFace;

    using FaceLateralSubControlVolumeFace = typename GridGeometry::Traits::FaceLateralSubControlVolumeFace;

    using Extrusion = Extrusion_t<GridGeometry>;

    using CellCenterPrimaryVariables = GetPropType<TypeTag, Properties::CellCenterPrimaryVariables>;

    using FacePrimaryVariables = GetPropType<TypeTag, Properties::FacePrimaryVariables>;

    using BoundaryTypes = typename ProblemTraits<Problem>::BoundaryTypes;

    using VelocityGradients = StaggeredVelocityGradients<Scalar, GridGeometry, BoundaryTypes, Indices>;


    static constexpr bool normalizePressure = getPropValue<TypeTag, Properties::NormalizePressure>();


    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;


    static constexpr auto cellCenterIdx = GridGeometry::cellCenterIdx();

    static constexpr auto faceIdx = GridGeometry::faceIdx();


    static constexpr int upwindSchemeOrder = getPropValue<TypeTag, Properties::UpwindSchemeOrder>();

    static constexpr bool useHigherOrder = upwindSchemeOrder > 1;


public:


    using HeatConductionType = GetPropType<TypeTag, Properties::HeatConductionType>;


    template<class UpwindTerm>

    [[deprecated("Will be removed after release 3.6. Use interface with additional fvGeometry parameter instead.")]]

    static Scalar advectiveFluxForCellCenter(const Problem& problem,

                                             const ElementVolumeVariables& elemVolVars,

                                             const ElementFaceVariables& elemFaceVars,

                                             const SubControlVolumeFace &scvf,

                                             UpwindTerm upwindTerm)

    {

        const Scalar velocity = elemFaceVars[scvf].velocitySelf();

        const bool insideIsUpstream = scvf.directionSign() == sign(velocity);

        static const Scalar upwindWeight = getParamFromGroup<Scalar>(problem.paramGroup(), "Flux.UpwindWeight");


        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];

        const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];


        const auto& upstreamVolVars = insideIsUpstream ? insideVolVars : outsideVolVars;

        const auto& downstreamVolVars = insideIsUpstream ? outsideVolVars : insideVolVars;


        const Scalar flux = (upwindWeight * upwindTerm(upstreamVolVars) +

                            (1.0 - upwindWeight) * upwindTerm(downstreamVolVars))

                            * velocity * Extrusion::area(scvf) * scvf.directionSign();


        return flux * extrusionFactor_(elemVolVars, scvf);

    }


    template<class UpwindTerm>

    static Scalar advectiveFluxForCellCenter(const Problem& problem,

                                             const FVElementGeometry& fvGeometry,

                                             const ElementVolumeVariables& elemVolVars,

                                             const ElementFaceVariables& elemFaceVars,

                                             const SubControlVolumeFace &scvf,

                                             UpwindTerm upwindTerm)

    {

        const Scalar velocity = elemFaceVars[scvf].velocitySelf();

        const bool insideIsUpstream = scvf.directionSign() == sign(velocity);

        static const Scalar upwindWeight = getParamFromGroup<Scalar>(problem.paramGroup(), "Flux.UpwindWeight");


        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];

        const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];


        const auto& upstreamVolVars = insideIsUpstream ? insideVolVars : outsideVolVars;

        const auto& downstreamVolVars = insideIsUpstream ? outsideVolVars : insideVolVars;


        const Scalar flux = (upwindWeight * upwindTerm(upstreamVolVars) +

                            (1.0 - upwindWeight) * upwindTerm(downstreamVolVars))

                            * velocity * Extrusion::area(fvGeometry, scvf) * scvf.directionSign();


        return flux * extrusionFactor_(elemVolVars, scvf);

    }


    CellCenterPrimaryVariables computeMassFlux(const Problem& problem,

                                               const Element& element,

                                               const FVElementGeometry& fvGeometry,

                                               const ElementVolumeVariables& elemVolVars,

                                               const ElementFaceVariables& elemFaceVars,

                                               const SubControlVolumeFace& scvf,

                                               const FluxVariablesCache& fluxVarsCache)

    {

        // The advectively transported quantity (i.e density for a single-phase system).

        auto upwindTerm = [](const auto& volVars) { return volVars.density(); };


        // Call the generic flux function.

        CellCenterPrimaryVariables result(0.0);

        result[Indices::conti0EqIdx - ModelTraits::dim()] = advectiveFluxForCellCenter(problem, fvGeometry, elemVolVars, elemFaceVars, scvf, upwindTerm);


        return result;

    }


    FacePrimaryVariables computeMomentumFlux(const Problem& problem,

                                             const Element& element,

                                             const SubControlVolumeFace& scvf,

                                             const FVElementGeometry& fvGeometry,

                                             const ElementVolumeVariables& elemVolVars,

                                             const ElementFaceVariables& elemFaceVars,

                                             const GridFluxVariablesCache& gridFluxVarsCache)

    {

        return computeFrontalMomentumFlux(problem, element, scvf, fvGeometry, elemVolVars, elemFaceVars, gridFluxVarsCache) +

               computeLateralMomentumFlux(problem, element, scvf, fvGeometry, elemVolVars, elemFaceVars, gridFluxVarsCache);

    }


    FacePrimaryVariables computeFrontalMomentumFlux(const Problem& problem,

                                                    const Element& element,

                                                    const SubControlVolumeFace& scvf,

                                                    const FVElementGeometry& fvGeometry,

                                                    const ElementVolumeVariables& elemVolVars,

                                                    const ElementFaceVariables& elemFaceVars,

                                                    const GridFluxVariablesCache& gridFluxVarsCache)

    {

        FacePrimaryVariables frontalFlux(0.0);


        // The velocities of the dof at interest and the one of the opposite scvf.

        const Scalar velocitySelf = elemFaceVars[scvf].velocitySelf();

        const Scalar velocityOpposite = elemFaceVars[scvf].velocityOpposite();

        const auto& faceVars =  elemFaceVars[scvf];


        // Advective flux.

        if (problem.enableInertiaTerms())

        {

            // Get the average velocity at the center of the element (i.e. the location of the staggered face).

            const Scalar transportingVelocity = (velocitySelf + velocityOpposite) * 0.5;

            const bool selfIsUpstream = scvf.directionSign() != sign(transportingVelocity);


            StaggeredUpwindHelper<TypeTag, upwindSchemeOrder> upwindHelper(element, fvGeometry, scvf, elemFaceVars, elemVolVars, gridFluxVarsCache.staggeredUpwindMethods());

            frontalFlux += upwindHelper.computeUpwindFrontalMomentum(selfIsUpstream)

                           * transportingVelocity * -1.0 * scvf.directionSign();

        }


        // The volume variables within the current element. We only require those (and none of neighboring elements)

        // because the fluxes are calculated over the staggered face at the center of the element.

        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];


        // Diffusive flux.

        const Scalar velocityGrad_ii = VelocityGradients::velocityGradII(scvf, faceVars) * scvf.directionSign();


        static const bool enableUnsymmetrizedVelocityGradient

            = getParamFromGroup<bool>(problem.paramGroup(), "FreeFlow.EnableUnsymmetrizedVelocityGradient", false);

        const Scalar factor = enableUnsymmetrizedVelocityGradient ? 1.0 : 2.0;

        frontalFlux -= factor * insideVolVars.effectiveViscosity() * velocityGrad_ii;


        // The pressure term.

        // If specified, the pressure can be normalized using the initial value on the scfv of interest.

        // The scvf is used to normalize by the same value from the left and right side.

        // Can potentially help to improve the condition number of the system matrix.

        const Scalar pressure = normalizePressure ?

                                insideVolVars.pressure() - problem.initial(scvf)[Indices::pressureIdx]

                              : insideVolVars.pressure();


        // Account for the orientation of the staggered face's normal outer normal vector

        // (pointing in opposite direction of the scvf's one).

        frontalFlux += pressure * -1.0 * scvf.directionSign();


        // Account for the staggered face's area. For rectangular elements, this equals the area of the scvf

        // our velocity dof of interest lives on but with adjusted centroid

        const auto& scv = fvGeometry.scv(scvf.insideScvIdx());

        FaceFrontalSubControlVolumeFace frontalFace(scv.center(), scvf.area());

        return frontalFlux * Extrusion::area(fvGeometry, frontalFace) * insideVolVars.extrusionFactor();

   }


    FacePrimaryVariables computeLateralMomentumFlux(const Problem& problem,

                                                    const Element& element,

                                                    const SubControlVolumeFace& scvf,

                                                    const FVElementGeometry& fvGeometry,

                                                    const ElementVolumeVariables& elemVolVars,

                                                    const ElementFaceVariables& elemFaceVars,

                                                    const GridFluxVariablesCache& gridFluxVarsCache)

    {

        FacePrimaryVariables lateralFlux(0.0);

        const auto& faceVars = elemFaceVars[scvf];

        const std::size_t numSubFaces = scvf.pairData().size();


        // If the current scvf is on a boundary, check if there is a Neumann BC for the stress in tangential direction.

        // Create a boundaryTypes object (will be empty if not at a boundary).

        std::optional<BoundaryTypes> currentScvfBoundaryTypes;

        if (scvf.boundary())

            currentScvfBoundaryTypes.emplace(problem.boundaryTypes(element, scvf));


        // Account for all sub faces.

        for (int localSubFaceIdx = 0; localSubFaceIdx < numSubFaces; ++localSubFaceIdx)

        {

            const auto eIdx = scvf.insideScvIdx();

            // Get the face normal to the face the dof lives on. The staggered sub face coincides with half of this lateral face.

            const auto& lateralFace = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx);


            // Create a boundaryTypes object (will be empty if not at a boundary).

            std::optional<BoundaryTypes> lateralFaceBoundaryTypes;


            // Check if there is face/element parallel to our face of interest where the dof lives on. If there is no parallel neighbor,

            // we are on a boundary where we have to check for boundary conditions.

            if (lateralFace.boundary())

            {

                // Retrieve the boundary types that correspond to the center of the lateral scvf. As a convention, we always query

                // the type of BCs at the center of the element's "actual" lateral scvf (not the face of the staggered control volume).

                // The value of the BC will be evaluated at the center of the staggered face.

                //     --------T######V                 || frontal face of staggered half-control-volume

                //     |      ||      | current scvf    #  lateral staggered face of interest (may lie on a boundary)

                //     |      ||      |                 x  dof position

                //     |      ||      x~~~~> vel.Self   -- element boundaries

                //     |      ||      |                 T  position at which the type of boundary conditions will be evaluated

                //     |      ||      |                    (center of lateral scvf)

                //     ----------------                 V  position at which the value of the boundary conditions will be evaluated

                //                                         (center of the staggered lateral face)

                lateralFaceBoundaryTypes.emplace(problem.boundaryTypes(element, lateralFace));

            }


            // If the current scvf is on a boundary and if there is a Neumann or Beavers-Joseph-(Saffmann) BC for the stress in tangential direction,

            // assign this value for the lateral momentum flux. No further calculations are required. We assume that all lateral faces

            // have the same type of BC (Neumann or Beavers-Joseph-(Saffmann)), but we sample the value at their actual positions.

            if (currentScvfBoundaryTypes)

            {

                // Handle Neumann BCs.

                if (currentScvfBoundaryTypes->isNeumann(Indices::velocity(lateralFace.directionIndex())))

                {

                    // Get the location of the lateral staggered face's center.

                    FaceLateralSubControlVolumeFace lateralScvf(lateralStaggeredSCVFCenter_(lateralFace, scvf, localSubFaceIdx), 0.5*lateralFace.area());

                    const auto& lateralStaggeredFaceCenter = lateralStaggeredFaceCenter_(scvf, localSubFaceIdx);

                    const auto lateralBoundaryFace = makeStaggeredBoundaryFace(scvf, lateralStaggeredFaceCenter);

                    lateralFlux += problem.neumann(element, fvGeometry, elemVolVars, elemFaceVars, lateralBoundaryFace)[Indices::velocity(lateralFace.directionIndex())]

                        * extrusionFactor_(elemVolVars, lateralFace) * Extrusion::area(fvGeometry, lateralScvf) * lateralFace.directionSign();


                    continue;

                }


                // Treat the edge case when our current scvf has a BJ condition while the lateral face has a Neumann BC.

                // It is not clear how to evaluate the BJ condition here.

                // For symmetry reasons, our own scvf should then have the same Neumann flux as the lateral face.

                // TODO: We should clarify if this is the correct approach.

                if (currentScvfBoundaryTypes->isBeaversJoseph(Indices::velocity(lateralFace.directionIndex())) && lateralFaceBoundaryTypes &&

                    lateralFaceBoundaryTypes->isNeumann(Indices::velocity(scvf.directionIndex())))

                {

                    FaceLateralSubControlVolumeFace lateralScvf(lateralStaggeredSCVFCenter_(lateralFace, scvf, localSubFaceIdx), 0.5*lateralFace.area());

                    const auto& lateralStaggeredFaceCenter = lateralStaggeredFaceCenter_(scvf, localSubFaceIdx);

                    const auto lateralBoundaryFace = makeStaggeredBoundaryFace(lateralFace, lateralStaggeredFaceCenter);

                    lateralFlux += problem.neumann(element, fvGeometry, elemVolVars, elemFaceVars, lateralBoundaryFace)[Indices::velocity(scvf.directionIndex())]

                        * extrusionFactor_(elemVolVars, lateralFace) * Extrusion::area(fvGeometry, lateralScvf) * lateralFace.directionSign();


                    continue;

                }

            }


            // Check if the lateral face (perpendicular to our current scvf) lies on a boundary. If yes, boundary conditions might need to be treated

            // and further calculations can be skipped.

            if (lateralFace.boundary())

            {

                // Check if we have a symmetry boundary condition. If yes, the tangential part of the momentum flux can be neglected

                // and we may skip any further calculations for the given sub face.

                if (lateralFaceBoundaryTypes->isSymmetry())

                    continue;


                // Handle Neumann boundary conditions. No further calculations are then required for the given sub face.

                if (lateralFaceBoundaryTypes->isNeumann(Indices::velocity(scvf.directionIndex())))

                {

                    // Construct a temporary scvf which corresponds to the staggered sub face, featuring the location

                    // the staggered faces's center.

                    FaceLateralSubControlVolumeFace lateralScvf(lateralStaggeredSCVFCenter_(lateralFace, scvf, localSubFaceIdx), 0.5*lateralFace.area());

                    const auto& lateralStaggeredFaceCenter = lateralStaggeredFaceCenter_(scvf, localSubFaceIdx);

                    const auto lateralBoundaryFace = makeStaggeredBoundaryFace(lateralFace, lateralStaggeredFaceCenter);

                    lateralFlux += problem.neumann(element, fvGeometry, elemVolVars, elemFaceVars, lateralBoundaryFace)[Indices::velocity(scvf.directionIndex())]

                                                  * elemVolVars[lateralFace.insideScvIdx()].extrusionFactor() * Extrusion::area(fvGeometry, lateralScvf);


                    continue;

                }


                // Handle wall-function fluxes (only required for RANS models)

                if (incorporateWallFunction_(lateralFlux, problem, element, fvGeometry, scvf, elemVolVars, elemFaceVars, localSubFaceIdx))

                    continue;

            }


            // Check the consistency of the boundary conditions, exactly one of the following must be set

            if (lateralFaceBoundaryTypes)

            {

                std::bitset<3> admittableBcTypes;

                admittableBcTypes.set(0, lateralFaceBoundaryTypes->isDirichlet(Indices::pressureIdx));

                admittableBcTypes.set(1, lateralFaceBoundaryTypes->isDirichlet(Indices::velocity(scvf.directionIndex())));

                admittableBcTypes.set(2, lateralFaceBoundaryTypes->isBeaversJoseph(Indices::velocity(scvf.directionIndex())));

                if (admittableBcTypes.count() != 1)

                {

                    DUNE_THROW(Dune::InvalidStateException, "Invalid boundary conditions for lateral scvf "

                    "for the momentum equations at global position " << lateralStaggeredFaceCenter_(scvf, localSubFaceIdx)

                    << ", current scvf global position " << scvf.center());

                }

            }


            // If none of the above boundary conditions apply for the given sub face, proceed to calculate the tangential momentum flux.

            if (problem.enableInertiaTerms())

                lateralFlux += computeAdvectivePartOfLateralMomentumFlux_(problem, fvGeometry, element,

                                                                          scvf, elemVolVars, elemFaceVars,

                                                                          gridFluxVarsCache,

                                                                          currentScvfBoundaryTypes, lateralFaceBoundaryTypes,

                                                                          localSubFaceIdx);


            lateralFlux += computeDiffusivePartOfLateralMomentumFlux_(problem, fvGeometry, element,

                                                                      scvf, elemVolVars, faceVars,

                                                                      currentScvfBoundaryTypes, lateralFaceBoundaryTypes,

                                                                      localSubFaceIdx);

        }

        return lateralFlux;

    }


    [[deprecated("Will be removed after release 3.6. Use interface with additional fvGeometry parameter instead.")]]

    FacePrimaryVariables inflowOutflowBoundaryFlux(const Problem& problem,

                                                   const Element& element,

                                                   const SubControlVolumeFace& scvf,

                                                   const ElementVolumeVariables& elemVolVars,

                                                   const ElementFaceVariables& elemFaceVars) const

    {

        FacePrimaryVariables inOrOutflow(0.0);

        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];


        // Advective momentum flux.

        if (problem.enableInertiaTerms())

        {

            const Scalar velocitySelf = elemFaceVars[scvf].velocitySelf();

            const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];

            const auto& upVolVars = (scvf.directionSign() == sign(velocitySelf)) ?

                                    insideVolVars : outsideVolVars;


            inOrOutflow += velocitySelf * velocitySelf * upVolVars.density();

        }


        // Apply a pressure at the boundary.

        const Scalar boundaryPressure = normalizePressure

                                        ? (problem.dirichlet(element, scvf)[Indices::pressureIdx] -

                                           problem.initial(scvf)[Indices::pressureIdx])

                                        : problem.dirichlet(element, scvf)[Indices::pressureIdx];

        inOrOutflow += boundaryPressure;


        // Account for the orientation of the face at the boundary,

        return inOrOutflow * scvf.directionSign() * Extrusion::area(scvf) * insideVolVars.extrusionFactor();

    }


    FacePrimaryVariables inflowOutflowBoundaryFlux(const Problem& problem,

                                                   const SubControlVolumeFace& scvf,

                                                   const FVElementGeometry& fvGeometry,

                                                   const ElementVolumeVariables& elemVolVars,

                                                   const ElementFaceVariables& elemFaceVars) const

    {

        FacePrimaryVariables inOrOutflow(0.0);

        const auto& element = fvGeometry.element();

        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];


        // Advective momentum flux.

        if (problem.enableInertiaTerms())

        {

            const Scalar velocitySelf = elemFaceVars[scvf].velocitySelf();

            const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];

            const auto& upVolVars = (scvf.directionSign() == sign(velocitySelf)) ?

                                    insideVolVars : outsideVolVars;


            inOrOutflow += velocitySelf * velocitySelf * upVolVars.density();

        }


        // Apply a pressure at the boundary.

        const Scalar boundaryPressure = normalizePressure

                                        ? (problem.dirichlet(element, scvf)[Indices::pressureIdx] -

                                           problem.initial(scvf)[Indices::pressureIdx])

                                        : problem.dirichlet(element, scvf)[Indices::pressureIdx];

        inOrOutflow += boundaryPressure;


        // Account for the orientation of the face at the boundary,

        return inOrOutflow * scvf.directionSign() * Extrusion::area(fvGeometry, scvf) * insideVolVars.extrusionFactor();

    }


private:


    FacePrimaryVariables computeAdvectivePartOfLateralMomentumFlux_(const Problem& problem,

                                                                    const FVElementGeometry& fvGeometry,

                                                                    const Element& element,

                                                                    const SubControlVolumeFace& scvf,

                                                                    const ElementVolumeVariables& elemVolVars,

                                                                    const ElementFaceVariables& elemFaceVars,

                                                                    const GridFluxVariablesCache& gridFluxVarsCache,

                                                                    const std::optional<BoundaryTypes>& currentScvfBoundaryTypes,

                                                                    const std::optional<BoundaryTypes>& lateralFaceBoundaryTypes,

                                                                    const int localSubFaceIdx)

    {

        const auto eIdx = scvf.insideScvIdx();

        const auto& lateralFace = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx);


        // Get the transporting velocity, located at the scvf perpendicular to the current scvf where the dof

        // of interest is located.

        const Scalar transportingVelocity = [&]()

        {

            const auto& faceVars = elemFaceVars[scvf];

            if (!scvf.boundary())

                return faceVars.velocityLateralInside(localSubFaceIdx);

            else

            {

                // Create a boundaryTypes object. Get the boundary conditions. We sample the type of BC at the center of the current scvf.

                const auto bcTypes = problem.boundaryTypes(element, scvf);


                if (bcTypes.isDirichlet(Indices::velocity(lateralFace.directionIndex())))

                {

                    // Construct a temporary scvf which corresponds to the staggered sub face, featuring the location

                    // the staggered faces's center.

                    const auto& lateralBoundaryFacePos = lateralStaggeredFaceCenter_(scvf, localSubFaceIdx);

                    const auto lateralBoundaryFace = makeStaggeredBoundaryFace(scvf, lateralBoundaryFacePos);

                    return problem.dirichlet(element, lateralBoundaryFace)[Indices::velocity(lateralFace.directionIndex())];

                }

                else if (bcTypes.isBeaversJoseph(Indices::velocity(lateralFace.directionIndex())))

                {

                    return VelocityGradients::beaversJosephVelocityAtCurrentScvf(problem, element, fvGeometry, scvf,  faceVars,

                                                                                 currentScvfBoundaryTypes, lateralFaceBoundaryTypes, localSubFaceIdx);

                }

                else

                    return faceVars.velocityLateralInside(localSubFaceIdx);

            }

        }();


        const bool selfIsUpstream = lateralFace.directionSign() == sign(transportingVelocity);

        StaggeredUpwindHelper<TypeTag, upwindSchemeOrder> upwindHelper(element, fvGeometry, scvf, elemFaceVars, elemVolVars, gridFluxVarsCache.staggeredUpwindMethods());

        FaceLateralSubControlVolumeFace lateralScvf(lateralStaggeredSCVFCenter_(lateralFace, scvf, localSubFaceIdx), 0.5*lateralFace.area());

        return upwindHelper.computeUpwindLateralMomentum(selfIsUpstream, lateralFace, localSubFaceIdx, currentScvfBoundaryTypes, lateralFaceBoundaryTypes)

               * transportingVelocity * lateralFace.directionSign() * Extrusion::area(fvGeometry, lateralScvf) * extrusionFactor_(elemVolVars, lateralFace);

    }


    FacePrimaryVariables computeDiffusivePartOfLateralMomentumFlux_(const Problem& problem,

                                                                    const FVElementGeometry& fvGeometry,

                                                                    const Element& element,

                                                                    const SubControlVolumeFace& scvf,

                                                                    const ElementVolumeVariables& elemVolVars,

                                                                    const FaceVariables& faceVars,

                                                                    const std::optional<BoundaryTypes>& currentScvfBoundaryTypes,

                                                                    const std::optional<BoundaryTypes>& lateralFaceBoundaryTypes,

                                                                    const int localSubFaceIdx)

    {

        const auto eIdx = scvf.insideScvIdx();

        const auto& lateralFace = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx);


        FacePrimaryVariables lateralDiffusiveFlux(0.0);


        static const bool enableUnsymmetrizedVelocityGradient

            = getParamFromGroup<bool>(problem.paramGroup(), "FreeFlow.EnableUnsymmetrizedVelocityGradient", false);


        // Get the volume variables of the own and the neighboring element. The neighboring

        // element is adjacent to the staggered face normal to the current scvf

        // where the dof of interest is located.

        const auto& insideVolVars = elemVolVars[lateralFace.insideScvIdx()];

        const auto& outsideVolVars = elemVolVars[lateralFace.outsideScvIdx()];


        // Get the averaged viscosity at the staggered face normal to the current scvf.

        const Scalar muAvg = lateralFace.boundary()

                             ? insideVolVars.effectiveViscosity()

                             : (insideVolVars.effectiveViscosity() + outsideVolVars.effectiveViscosity()) * 0.5;


        // Consider the shear stress caused by the gradient of the velocities normal to our face of interest.

        if (!enableUnsymmetrizedVelocityGradient)

        {

            if (!scvf.boundary() ||

                currentScvfBoundaryTypes->isDirichlet(Indices::velocity(lateralFace.directionIndex())) ||

                currentScvfBoundaryTypes->isBeaversJoseph(Indices::velocity(lateralFace.directionIndex())))

            {

                const Scalar velocityGrad_ji = VelocityGradients::velocityGradJI(problem, element, fvGeometry, scvf, faceVars, currentScvfBoundaryTypes, lateralFaceBoundaryTypes, localSubFaceIdx);

                // Account for the orientation of the staggered normal face's outer normal vector.

                lateralDiffusiveFlux -= muAvg * velocityGrad_ji * lateralFace.directionSign();

            }

        }


        // Consider the shear stress caused by the gradient of the velocities parallel to our face of interest.

        // If we have a Dirichlet condition for the pressure at the lateral face we assume to have a zero velocityGrad_ij velocity gradient

        // so we can skip the computation.

        if (!lateralFace.boundary() || !lateralFaceBoundaryTypes->isDirichlet(Indices::pressureIdx))

        {

            const Scalar velocityGrad_ij = VelocityGradients::velocityGradIJ(problem, element, fvGeometry, scvf, faceVars, currentScvfBoundaryTypes, lateralFaceBoundaryTypes, localSubFaceIdx);

            lateralDiffusiveFlux -= muAvg * velocityGrad_ij * lateralFace.directionSign();

        }


        // Account for the area of the staggered lateral face (0.5 of the coinciding scfv).

        FaceLateralSubControlVolumeFace lateralScvf(lateralStaggeredSCVFCenter_(lateralFace, scvf, localSubFaceIdx), 0.5*lateralFace.area());

        return lateralDiffusiveFlux * Extrusion::area(fvGeometry, lateralScvf) * extrusionFactor_(elemVolVars, lateralFace);

    }


    const GlobalPosition& lateralStaggeredFaceCenter_(const SubControlVolumeFace& scvf, const int localSubFaceIdx) const

    {

        return scvf.pairData(localSubFaceIdx).lateralStaggeredFaceCenter;

    };


    GlobalPosition lateralStaggeredSCVFCenter_(const SubControlVolumeFace& lateralFace,

                                               const SubControlVolumeFace& currentFace,

                                               const int localSubFaceIdx) const

    {

        auto pos = lateralStaggeredFaceCenter_(currentFace, localSubFaceIdx) + lateralFace.center();

        pos *= 0.5;

        return pos;

    }


    static Scalar extrusionFactor_(const ElementVolumeVariables& elemVolVars, const SubControlVolumeFace& scvf)

    {

        const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];

        const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];

        return harmonicMean(insideVolVars.extrusionFactor(), outsideVolVars.extrusionFactor());

    }


    template<class ...Args, bool turbulenceModel = ModelTraits::usesTurbulenceModel(), std::enable_if_t<!turbulenceModel, int> = 0>

    bool incorporateWallFunction_(Args&&... args) const

    { return false; }


    template<bool turbulenceModel = ModelTraits::usesTurbulenceModel(), std::enable_if_t<turbulenceModel, int> = 0>

    bool incorporateWallFunction_(FacePrimaryVariables& lateralFlux,

                                  const Problem& problem,

                                  const Element& element,

                                  const FVElementGeometry& fvGeometry,

                                  const SubControlVolumeFace& scvf,

                                  const ElementVolumeVariables& elemVolVars,

                                  const ElementFaceVariables& elemFaceVars,

                                  const std::size_t localSubFaceIdx) const

    {

        const auto eIdx = scvf.insideScvIdx();

        const auto& lateralFace = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx);


        if (problem.useWallFunction(element, lateralFace, Indices::velocity(scvf.directionIndex())))

        {

            FaceLateralSubControlVolumeFace lateralScvf(lateralStaggeredSCVFCenter_(lateralFace, scvf, localSubFaceIdx), 0.5*lateralFace.area());

            const auto lateralBoundaryFace = makeStaggeredBoundaryFace(lateralFace, lateralStaggeredFaceCenter_(scvf, localSubFaceIdx));

            lateralFlux += problem.wallFunction(element, fvGeometry, elemVolVars, elemFaceVars, scvf, lateralBoundaryFace)[Indices::velocity(scvf.directionIndex())]

                                               * extrusionFactor_(elemVolVars, lateralFace) * Extrusion::area(fvGeometry, lateralScvf);

            return true;

        }

        else

            return false;

    }

};


} // end namespace Dumux


#endif

exceptions.hh
Some exceptions thrown in DuMux

parameters.hh
The infrastructure to retrieve run-time parameters from Dune::ParameterTrees.

math.hh
Define some often used mathematical functions.

extrusion.hh
Helper classes to compute the integration elements.

method.hh
The available discretization methods in Dumux.

fluxvariablesbase.hh
Base class for the flux variables living on a sub control volume face.

staggeredupwindhelper.hh

Dumux::makeStaggeredBoundaryFace
SubControlVolumeFace makeStaggeredBoundaryFace(const SubControlVolumeFace &scvf, const typename SubControlVolumeFace::GlobalPosition &newCenter)
Helper function to turn a given cell scvface into a fake boundary face.
Definition: discretization/staggered/freeflow/subcontrolvolumeface.hh:104

Dumux::harmonicMean
constexpr Scalar harmonicMean(Scalar x, Scalar y, Scalar wx=1.0, Scalar wy=1.0) noexcept
Calculate the (weighted) harmonic mean of two scalar values.
Definition: math.hh:69

Dumux::sign
constexpr int sign(const ValueType &value) noexcept
Sign or signum function.
Definition: math.hh:641

Dumux
Adaption of the non-isothermal two-phase two-component flow model to problems with CO2.
Definition: adapt.hh:29

Dumux::Extrusion_t
typename Extrusion< T >::type Extrusion_t
Convenience alias for obtaining the extrusion type.
Definition: extrusion.hh:251

Dumux::GetPropType
typename GetProp< TypeTag, Property >::type GetPropType
get the type alias defined in the property
Definition: propertysystem.hh:180

Dumux::IOName::pressure
std::string pressure(int phaseIdx) noexcept
I/O name of pressure for multiphase systems.
Definition: name.hh:34

Dumux::ProblemTraits::BoundaryTypes
typename Detail::template ProblemTraits< Problem, typename GridGeometry::DiscretizationMethod >::BoundaryTypes BoundaryTypes
Definition: common/typetraits/problem.hh:46

Dumux::FluxVariablesBase
Base class for the flux variables living on a sub control volume face.
Definition: fluxvariablesbase.hh:45

Dumux::NavierStokesFluxVariablesImpl
The flux variables class for the Navier-Stokes model using the staggered grid discretization.
Definition: freeflow/navierstokes/fluxvariables.hh:35

Dumux::StaggeredVelocityGradients
Helper class for calculating the velocity gradients for the Navier-Stokes model using the staggered g...
Definition: momentum/velocitygradients.hh:58

Dumux::NavierStokesFluxVariablesImpl< TypeTag, DiscretizationMethods::Staggered >::advectiveFluxForCellCenter
static Scalar advectiveFluxForCellCenter(const Problem &problem, const FVElementGeometry &fvGeometry, const ElementVolumeVariables &elemVolVars, const ElementFaceVariables &elemFaceVars, const SubControlVolumeFace &scvf, UpwindTerm upwindTerm)
Returns the advective flux over a sub control volume face.
Definition: freeflow/navierstokes/staggered/fluxvariables.hh:149

Dumux::NavierStokesFluxVariablesImpl< TypeTag, DiscretizationMethods::Staggered >::computeLateralMomentumFlux
FacePrimaryVariables computeLateralMomentumFlux(const Problem &problem, const Element &element, const SubControlVolumeFace &scvf, const FVElementGeometry &fvGeometry, const ElementVolumeVariables &elemVolVars, const ElementFaceVariables &elemFaceVars, const GridFluxVariablesCache &gridFluxVarsCache)
Returns the momentum flux over the staggered faces perpendicular to the scvf where the velocity dof o...
Definition: freeflow/navierstokes/staggered/fluxvariables.hh:313

Dumux::NavierStokesFluxVariablesImpl< TypeTag, DiscretizationMethods::Staggered >::inflowOutflowBoundaryFlux
FacePrimaryVariables inflowOutflowBoundaryFlux(const Problem &problem, const SubControlVolumeFace &scvf, const FVElementGeometry &fvGeometry, const ElementVolumeVariables &elemVolVars, const ElementFaceVariables &elemFaceVars) const
Returns the momentum flux over an inflow or outflow boundary face.
Definition: freeflow/navierstokes/staggered/fluxvariables.hh:517

Dumux::NavierStokesFluxVariablesImpl< TypeTag, DiscretizationMethods::Staggered >::computeFrontalMomentumFlux
FacePrimaryVariables computeFrontalMomentumFlux(const Problem &problem, const Element &element, const SubControlVolumeFace &scvf, const FVElementGeometry &fvGeometry, const ElementVolumeVariables &elemVolVars, const ElementFaceVariables &elemFaceVars, const GridFluxVariablesCache &gridFluxVarsCache)
Returns the frontal part of the momentum flux. This treats the flux over the staggered face at the ce...
Definition: freeflow/navierstokes/staggered/fluxvariables.hh:238

Dumux::NavierStokesFluxVariablesImpl< TypeTag, DiscretizationMethods::Staggered >::advectiveFluxForCellCenter
static Scalar advectiveFluxForCellCenter(const Problem &problem, const ElementVolumeVariables &elemVolVars, const ElementFaceVariables &elemFaceVars, const SubControlVolumeFace &scvf, UpwindTerm upwindTerm)
Returns the advective flux over a sub control volume face.
Definition: freeflow/navierstokes/staggered/fluxvariables.hh:116

Dumux::NavierStokesFluxVariablesImpl< TypeTag, DiscretizationMethods::Staggered >::computeMomentumFlux
FacePrimaryVariables computeMomentumFlux(const Problem &problem, const Element &element, const SubControlVolumeFace &scvf, const FVElementGeometry &fvGeometry, const ElementVolumeVariables &elemVolVars, const ElementFaceVariables &elemFaceVars, const GridFluxVariablesCache &gridFluxVarsCache)
Returns the momentum flux over all staggered faces.
Definition: freeflow/navierstokes/staggered/fluxvariables.hh:209

Dumux::NavierStokesFluxVariablesImpl< TypeTag, DiscretizationMethods::Staggered >::inflowOutflowBoundaryFlux
FacePrimaryVariables inflowOutflowBoundaryFlux(const Problem &problem, const Element &element, const SubControlVolumeFace &scvf, const ElementVolumeVariables &elemVolVars, const ElementFaceVariables &elemFaceVars) const
Returns the momentum flux over an inflow or outflow boundary face.
Definition: freeflow/navierstokes/staggered/fluxvariables.hh:470

Dumux::NavierStokesFluxVariablesImpl< TypeTag, DiscretizationMethods::Staggered >::HeatConductionType
GetPropType< TypeTag, Properties::HeatConductionType > HeatConductionType
Definition: freeflow/navierstokes/staggered/fluxvariables.hh:104

Dumux::NavierStokesFluxVariablesImpl< TypeTag, DiscretizationMethods::Staggered >::computeMassFlux
CellCenterPrimaryVariables computeMassFlux(const Problem &problem, const Element &element, const FVElementGeometry &fvGeometry, const ElementVolumeVariables &elemVolVars, const ElementFaceVariables &elemFaceVars, const SubControlVolumeFace &scvf, const FluxVariablesCache &fluxVarsCache)
Computes the flux for the cell center residual (mass balance).
Definition: freeflow/navierstokes/staggered/fluxvariables.hh:188

Dumux::StaggeredUpwindHelper
The upwinding variables class for the Navier-Stokes model using the staggered grid discretization.
Definition: staggeredupwindhelper.hh:48

Dumux::StaggeredUpwindHelper::computeUpwindFrontalMomentum
FacePrimaryVariables computeUpwindFrontalMomentum(const bool selfIsUpstream) const
Returns the momentum in the frontal direction.
Definition: staggeredupwindhelper.hh:115

properties.hh
Declares all properties used in Dumux.

problem.hh
Type traits for problem classes.

velocitygradients.hh