freeflow/rans/problem.hh

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#ifndef DUMUX_RANS_PROBLEM_HH
#define DUMUX_RANS_PROBLEM_HH
 
#include <dune/common/fmatrix.hh>
#include <dumux/common/properties.hh>
#include <dumux/common/staggeredfvproblem.hh>
#include <dumux/discretization/localview.hh>
#include <dumux/discretization/staggered/elementsolution.hh>
#include <dumux/discretization/method.hh>
#include <dumux/freeflow/navierstokes/problem.hh>
 
#include "model.hh"
 
namespace Dumux {

template<class TypeTag, TurbulenceModel turbulenceModel>
class RANSProblemImpl;

template<class TypeTag>
using RANSProblem = RANSProblemImpl<TypeTag, GetPropType<TypeTag, Properties::ModelTraits>::turbulenceModel()>;

template<class TypeTag>
class RANSProblemBase : public NavierStokesProblem<TypeTag>
{
    using ParentType = NavierStokesProblem<TypeTag>;
    using Implementation = GetPropType<TypeTag, Properties::Problem>;
 
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
 
    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 VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
    using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
    using PrimaryVariables = typename VolumeVariables::PrimaryVariables;
    using CellCenterPrimaryVariables = GetPropType<TypeTag, Properties::CellCenterPrimaryVariables>;
    using FacePrimaryVariables = GetPropType<TypeTag, Properties::FacePrimaryVariables>;
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
 
    using GlobalPosition = typename SubControlVolumeFace::GlobalPosition;
 
    static constexpr auto dim = GridView::dimension;
    using DimVector = GlobalPosition;
    using DimMatrix = Dune::FieldMatrix<Scalar, dim, dim>;
 
public:
    RANSProblemBase(std::shared_ptr<const GridGeometry> gridGeometry, const std::string& paramGroup = "")
    : ParentType(gridGeometry, paramGroup)
    { }

    void updateStaticWallProperties()
    {
        using std::abs;
        std::cout << "Update static wall properties. ";
        calledUpdateStaticWallProperties = true;
 
        // update size and initial values of the global vectors
        wallElementIdx_.resize(this->gridGeometry().elementMapper().size());
        wallDistance_.resize(this->gridGeometry().elementMapper().size(), std::numeric_limits<Scalar>::max());
        neighborIdx_.resize(this->gridGeometry().elementMapper().size());
        cellCenter_.resize(this->gridGeometry().elementMapper().size(), GlobalPosition(0.0));
        velocity_.resize(this->gridGeometry().elementMapper().size(), DimVector(0.0));
        velocityMaximum_.resize(this->gridGeometry().elementMapper().size(), DimVector(0.0));
        velocityGradients_.resize(this->gridGeometry().elementMapper().size(), DimMatrix(0.0));
        stressTensorScalarProduct_.resize(this->gridGeometry().elementMapper().size(), 0.0);
        vorticityTensorScalarProduct_.resize(this->gridGeometry().elementMapper().size(), 0.0);
        flowNormalAxis_.resize(this->gridGeometry().elementMapper().size(), 0);
        wallNormalAxis_.resize(this->gridGeometry().elementMapper().size(), 1);
        kinematicViscosity_.resize(this->gridGeometry().elementMapper().size(), 0.0);
        sandGrainRoughness_.resize(this->gridGeometry().elementMapper().size(), 0.0);
 
        // retrieve all wall intersections and corresponding elements
        std::vector<unsigned int> wallElements;
        std::vector<GlobalPosition> wallPositions;
        std::vector<unsigned int> wallNormalAxisTemp;
 
        const auto gridView = this->gridGeometry().gridView();
        auto fvGeometry = localView(this->gridGeometry());
 
        for (const auto& element : elements(gridView))
        {
            fvGeometry.bindElement(element);
            for (const auto& scvf : scvfs(fvGeometry))
            {
                // only search for walls at a global boundary
                if (!scvf.boundary())
                    continue;
 
                if (asImp_().isOnWall(scvf))
                {
                    wallElements.push_back(this->gridGeometry().elementMapper().index(element));
                    wallPositions.push_back(scvf.center());
                    wallNormalAxisTemp.push_back(scvf.directionIndex());
                }
            }
        }
        std::cout << "NumWallIntersections=" << wallPositions.size() << std::endl;
        if (wallPositions.size() == 0)
            DUNE_THROW(Dune::InvalidStateException,
                       "No wall intersections have been found. Make sure that the isOnWall(globalPos) is working properly.");
 
 
        // search for shortest distance to wall for each element
        for (const auto& element : elements(gridView))
        {
            unsigned int elementIdx = this->gridGeometry().elementMapper().index(element);
            cellCenter_[elementIdx] = element.geometry().center();
            for (unsigned int i = 0; i < wallPositions.size(); ++i)
            {
                static const int problemWallNormalAxis
                    = getParamFromGroup<int>(this->paramGroup(), "RANS.WallNormalAxis", -1);
                int searchAxis = problemWallNormalAxis;
 
                // search along wall normal axis of the intersection
                if (problemWallNormalAxis < 0 || problemWallNormalAxis >= dim)
                {
                    searchAxis = wallNormalAxisTemp[i];
                }
 
                GlobalPosition global = element.geometry().center();
                global -= wallPositions[i];
                // second and argument ensures to use only aligned elements
                if (abs(global[searchAxis]) < wallDistance_[elementIdx]
                    && abs(global[searchAxis]) < global.two_norm() + 1e-8
                    && abs(global[searchAxis]) > global.two_norm() - 1e-8)
                {
                    wallDistance_[elementIdx] = abs(global[searchAxis]);
                    wallElementIdx_[elementIdx] = wallElements[i];
                    wallNormalAxis_[elementIdx] = searchAxis;
                    sandGrainRoughness_[elementIdx] = asImp_().sandGrainRoughnessAtPos(wallPositions[i]);
                }
            }
        }
 
        // search for neighbor Idxs
        for (const auto& element : elements(gridView))
        {
            unsigned int elementIdx = this->gridGeometry().elementMapper().index(element);
            for (unsigned int dimIdx = 0; dimIdx < dim; ++dimIdx)
            {
                neighborIdx_[elementIdx][dimIdx][0] = elementIdx;
                neighborIdx_[elementIdx][dimIdx][1] = elementIdx;
            }
 
            for (const auto& intersection : intersections(gridView, element))
            {
                if (intersection.boundary())
                    continue;
 
                unsigned int neighborIdx = this->gridGeometry().elementMapper().index(intersection.outside());
                for (unsigned int dimIdx = 0; dimIdx < dim; ++dimIdx)
                {
                    if (abs(cellCenter_[elementIdx][dimIdx] - cellCenter_[neighborIdx][dimIdx]) > 1e-8)
                    {
                        if (cellCenter_[elementIdx][dimIdx] > cellCenter_[neighborIdx][dimIdx])
                        {
                            neighborIdx_[elementIdx][dimIdx][0] = neighborIdx;
                        }
                        if (cellCenter_[elementIdx][dimIdx] < cellCenter_[neighborIdx][dimIdx])
                        {
                            neighborIdx_[elementIdx][dimIdx][1] = neighborIdx;
                        }
                    }
                }
            }
        }
    }

    void updateDynamicWallProperties(const SolutionVector& curSol)
    {
        using std::abs;
        using std::max;
        using std::min;
        std::cout << "Update dynamic wall properties." << std::endl;
        if (!calledUpdateStaticWallProperties)
            DUNE_THROW(Dune::InvalidStateException,
                       "You have to call updateStaticWallProperties() once before you call updateDynamicWallProperties().");
 
        static const int flowNormalAxis
            = getParamFromGroup<int>(this->paramGroup(), "RANS.FlowNormalAxis", -1);
 
        // re-initialize min and max values
        velocityMaximum_.assign(this->gridGeometry().elementMapper().size(), DimVector(1e-16));
        velocityMinimum_.assign(this->gridGeometry().elementMapper().size(), DimVector(std::numeric_limits<Scalar>::max()));
 
        // calculate cell-center-averaged velocities
        for (const auto& element : elements(this->gridGeometry().gridView()))
        {
            auto fvGeometry = localView(this->gridGeometry());
            fvGeometry.bindElement(element);
            unsigned int elementIdx = this->gridGeometry().elementMapper().index(element);
 
            // calculate velocities
            DimVector velocityTemp(0.0);
            for (auto&& scvf : scvfs(fvGeometry))
            {
                const int dofIdxFace = scvf.dofIndex();
                const auto numericalSolutionFace = curSol[GridGeometry::faceIdx()][dofIdxFace][Indices::velocity(scvf.directionIndex())];
                velocityTemp[scvf.directionIndex()] += numericalSolutionFace;
            }
            for (unsigned int dimIdx = 0; dimIdx < dim; ++dimIdx)
                velocity_[elementIdx][dimIdx] = velocityTemp[dimIdx] * 0.5; // faces are equidistant to cell center
        }
 
        // calculate cell-center-averaged velocity gradients, maximum, and minimum values
        for (const auto& element : elements(this->gridGeometry().gridView()))
        {
            unsigned int elementIdx = this->gridGeometry().elementMapper().index(element);
            unsigned int wallElementIdx = wallElementIdx_[elementIdx];
 
            Scalar maxVelocity = 0.0;
            for (unsigned int dimIdx = 0; dimIdx < dim; ++dimIdx)
            {
                for (unsigned int velIdx = 0; velIdx < dim; ++velIdx)
                {
                    velocityGradients_[elementIdx][velIdx][dimIdx]
                        = (velocity_[neighborIdx_[elementIdx][dimIdx][1]][velIdx]
                              - velocity_[neighborIdx_[elementIdx][dimIdx][0]][velIdx])
                          / (cellCenter_[neighborIdx_[elementIdx][dimIdx][1]][dimIdx]
                              - cellCenter_[neighborIdx_[elementIdx][dimIdx][0]][dimIdx]);
                    if (abs(cellCenter_[neighborIdx_[elementIdx][dimIdx][1]][dimIdx]
                            - cellCenter_[neighborIdx_[elementIdx][dimIdx][0]][dimIdx]) < 1e-8)
                        velocityGradients_[elementIdx][velIdx][dimIdx] = 0.0;
                }
 
                if (abs(velocity_[elementIdx][dimIdx]) > abs(velocityMaximum_[wallElementIdx][dimIdx]))
                {
                    velocityMaximum_[wallElementIdx][dimIdx] = velocity_[elementIdx][dimIdx];
                }
                if (abs(velocity_[elementIdx][dimIdx]) < abs(velocityMinimum_[wallElementIdx][dimIdx]))
                {
                    velocityMinimum_[wallElementIdx][dimIdx] = velocity_[elementIdx][dimIdx];
                }
 
                if (0 <= flowNormalAxis && flowNormalAxis < dim)
                {
                    flowNormalAxis_[elementIdx] = flowNormalAxis;
                }
                else if (abs(maxVelocity) < abs(velocity_[elementIdx][dimIdx]))
                {
                    maxVelocity = abs(velocity_[elementIdx][dimIdx]);
                    flowNormalAxis_[elementIdx] = dimIdx;
                }
            }
 
            auto fvGeometry = localView(this->gridGeometry());
            fvGeometry.bindElement(element);
            for (auto&& scvf : scvfs(fvGeometry))
            {
                // adapt calculations for Dirichlet condition
                unsigned int scvfNormDim = scvf.directionIndex();
                if (scvf.boundary())
                {
                    for (unsigned int velIdx = 0; velIdx < dim; ++velIdx)
                    {
                        if (!asImp_().boundaryTypes(element, scvf).isDirichlet(Indices::velocity(velIdx)))
                            continue;
 
                        Scalar dirichletVelocity = asImp_().dirichlet(element, scvf)[Indices::velocity(velIdx)];
 
                        unsigned int neighborIdx = neighborIdx_[elementIdx][scvfNormDim][0];
                        if (scvf.center()[scvfNormDim] < cellCenter_[elementIdx][scvfNormDim])
                            neighborIdx = neighborIdx_[elementIdx][scvfNormDim][1];
 
                        velocityGradients_[elementIdx][velIdx][scvfNormDim]
                            = (velocity_[neighborIdx][velIdx] - dirichletVelocity)
                              / (cellCenter_[neighborIdx][scvfNormDim] - scvf.center()[scvfNormDim]);
                    }
                }
 
                // Calculate the BJS-velocity by accounting for all sub faces.
                std::vector<int> bjsNumFaces(dim, 0);
                std::vector<unsigned int> bjsNeighbor(dim, 0);
                DimVector bjsVelocityAverage(0.0);
                DimVector normalNormCoordinate(0.0);
                unsigned int velIdx = Indices::velocity(scvfNormDim);
                const int numSubFaces = scvf.pairData().size();
                for(int localSubFaceIdx = 0; localSubFaceIdx < numSubFaces; ++localSubFaceIdx)
                {
                    const auto& lateralFace = fvGeometry.scvf(scvf.insideScvIdx(), scvf.pairData()[localSubFaceIdx].localLateralFaceIdx);
 
                    // adapt calculations for Beavers-Joseph-Saffman condition
                    unsigned int normalNormDim = lateralFace.directionIndex();
                    if (lateralFace.boundary() && (asImp_().boundaryTypes(element, lateralFace).isBeaversJoseph(Indices::velocity(velIdx))))
                    {
                        unsigned int neighborIdx = neighborIdx_[elementIdx][normalNormDim][0];
                        if (lateralFace.center()[normalNormDim] < cellCenter_[elementIdx][normalNormDim])
                            neighborIdx = neighborIdx_[elementIdx][normalNormDim][1];
 
                        const SubControlVolume& scv = fvGeometry.scv(scvf.insideScvIdx());
                        bjsVelocityAverage[normalNormDim] += ParentType::beaversJosephVelocity(element, scv, scvf, lateralFace, velocity_[elementIdx][velIdx], 0.0);
                        if (bjsNumFaces[normalNormDim] > 0 && neighborIdx != bjsNeighbor[normalNormDim])
                            DUNE_THROW(Dune::InvalidStateException, "Two different neighborIdx should not occur");
                        bjsNeighbor[normalNormDim] = neighborIdx;
                        normalNormCoordinate[normalNormDim] = lateralFace.center()[normalNormDim];
                        bjsNumFaces[normalNormDim]++;
                    }
                }
                for (unsigned dirIdx = 0; dirIdx < dim; ++dirIdx)
                {
                    if (bjsNumFaces[dirIdx] == 0)
                        continue;
 
                    unsigned int neighborIdx = bjsNeighbor[dirIdx];
                    bjsVelocityAverage[dirIdx] /= bjsNumFaces[dirIdx];
 
                    velocityGradients_[elementIdx][velIdx][dirIdx]
                        = (velocity_[neighborIdx][velIdx] - bjsVelocityAverage[dirIdx])
                          / (cellCenter_[neighborIdx][dirIdx] - normalNormCoordinate[dirIdx]);
 
                }
            }
        }
 
        // calculate or call all secondary variables
        for (const auto& element : elements(this->gridGeometry().gridView()))
        {
            unsigned int elementIdx = this->gridGeometry().elementMapper().index(element);
 
            Dune::FieldMatrix<Scalar, GridView::dimension, GridView::dimension> stressTensor(0.0);
            for (unsigned int dimIdx = 0; dimIdx < dim; ++dimIdx)
            {
                for (unsigned int velIdx = 0; velIdx < dim; ++velIdx)
                {
                    stressTensor[dimIdx][velIdx] = 0.5 * velocityGradients_[elementIdx][dimIdx][velIdx]
                                                   + 0.5 * velocityGradients_[elementIdx][velIdx][dimIdx];
              }
            }
            stressTensorScalarProduct_[elementIdx] = 0.0;
            for (unsigned int dimIdx = 0; dimIdx < dim; ++dimIdx)
            {
                for (unsigned int velIdx = 0; velIdx < dim; ++velIdx)
                {
                    stressTensorScalarProduct_[elementIdx] += stressTensor[dimIdx][velIdx] * stressTensor[dimIdx][velIdx];
                }
            }
 
            Dune::FieldMatrix<Scalar, GridView::dimension, GridView::dimension> vorticityTensor(0.0);
            for (unsigned int dimIdx = 0; dimIdx < dim; ++dimIdx)
            {
                for (unsigned int velIdx = 0; velIdx < dim; ++velIdx)
                {
                    vorticityTensor[dimIdx][velIdx] = 0.5 * velocityGradients_[elementIdx][dimIdx][velIdx]
                                                      - 0.5 * velocityGradients_[elementIdx][velIdx][dimIdx];
              }
            }
            vorticityTensorScalarProduct_[elementIdx] = 0.0;
            for (unsigned int dimIdx = 0; dimIdx < dim; ++dimIdx)
            {
                for (unsigned int velIdx = 0; velIdx < dim; ++velIdx)
                {
                    vorticityTensorScalarProduct_[elementIdx] += vorticityTensor[dimIdx][velIdx] * vorticityTensor[dimIdx][velIdx];
                }
            }
 
            auto fvGeometry = localView(this->gridGeometry());
            fvGeometry.bindElement(element);
            for (auto&& scv : scvs(fvGeometry))
            {
                const int dofIdx = scv.dofIndex();
 
                // construct a privars object from the cell center solution vector
                const auto& cellCenterPriVars = curSol[GridGeometry::cellCenterIdx()][dofIdx];
                PrimaryVariables priVars = makePriVarsFromCellCenterPriVars<PrimaryVariables>(cellCenterPriVars);
                auto elemSol = elementSolution<typename GridGeometry::LocalView>(std::move(priVars));
 
                VolumeVariables volVars;
                volVars.update(elemSol, asImp_(), element, scv);
                kinematicViscosity_[elementIdx] = volVars.viscosity() / volVars.density();
            }
        }
    }

    bool useWallFunction(const Element& element,
                         const SubControlVolumeFace& scvf,
                         const int& eqIdx) const
    { return false; }

    template<class ElementVolumeVariables, class ElementFaceVariables>
    FacePrimaryVariables wallFunction(const Element& element,
                                      const FVElementGeometry& fvGeometry,
                                      const ElementVolumeVariables& elemVolVars,
                                      const ElementFaceVariables& elemFaceVars,
                                      const SubControlVolumeFace& scvf,
                                      const SubControlVolumeFace& lateralBoundaryFace) const
    { return FacePrimaryVariables(0.0); }

    template<class ElementVolumeVariables, class ElementFaceVariables>
    CellCenterPrimaryVariables wallFunction(const Element& element,
                                            const FVElementGeometry& fvGeometry,
                                            const ElementVolumeVariables& elemVolVars,
                                            const ElementFaceVariables& elemFaceVars,
                                            const SubControlVolumeFace& scvf) const
    { return CellCenterPrimaryVariables(0.0); }

    bool isOnWall(const SubControlVolumeFace& scvf) const
    {
        return asImp_().isOnWallAtPos(scvf.center());
    }

    bool isOnWallAtPos(const GlobalPosition &globalPos) const
    {
        // Throw an exception if no walls are implemented
        DUNE_THROW(Dune::InvalidStateException,
                   "The problem does not provide an isOnWall() method.");
    }

    Scalar sandGrainRoughnessAtPos(const GlobalPosition &globalPos) const
    {
        return 0.0;
    }

    const Scalar karmanConstant() const
    { return 0.41; }

    const Scalar betaOmega() const
    {
        return 0.0708;
    }

    Scalar turbulentPrandtlNumber() const
    {
        static const Scalar turbulentPrandtlNumber
            = getParamFromGroup<Scalar>(this->paramGroup(), "RANS.TurbulentPrandtlNumber", 1.0);
        return turbulentPrandtlNumber;
    }

    Scalar turbulentSchmidtNumber() const
    {
        static const Scalar turbulentSchmidtNumber
            = getParamFromGroup<Scalar>(this->paramGroup(), "RANS.TurbulentSchmidtNumber", 1.0);
        return turbulentSchmidtNumber;
    }
 
public:
    bool calledUpdateStaticWallProperties = false;
    std::vector<unsigned int> wallElementIdx_;
    std::vector<Scalar> wallDistance_;
    std::vector<std::array<std::array<unsigned int, 2>, dim>> neighborIdx_;
    std::vector<GlobalPosition> cellCenter_;
    std::vector<DimVector> velocity_;
    std::vector<DimVector> velocityMaximum_;
    std::vector<DimVector> velocityMinimum_;
    std::vector<DimMatrix> velocityGradients_;
    std::vector<Scalar> stressTensorScalarProduct_;
    std::vector<Scalar> vorticityTensorScalarProduct_;
    std::vector<unsigned int> wallNormalAxis_;
    std::vector<unsigned int> flowNormalAxis_;
    std::vector<Scalar> kinematicViscosity_;
    std::vector<Scalar> sandGrainRoughness_;
 
private:
    Implementation &asImp_()
    { return *static_cast<Implementation *>(this); }

    const Implementation &asImp_() const
    { return *static_cast<const Implementation *>(this); }
};
 
} // end namespace Dumux
 
#endif