test/freeflow/navierstokes/channel/1d/problem.hh

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#ifndef DUMUX_DONEA_TEST_PROBLEM_HH
#define DUMUX_DONEA_TEST_PROBLEM_HH
 
#include <dune/common/fmatrix.hh>
#include <dune/grid/yaspgrid.hh>
 
#include <dumux/material/components/constant.hh>
#include <dumux/material/fluidsystems/1pliquid.hh>
 
#include <dumux/discretization/staggered/freeflow/properties.hh>
#include <dumux/freeflow/navierstokes/model.hh>
#include <dumux/freeflow/navierstokes/problem.hh>
#include "../../l2error.hh"
 
 
namespace Dumux {
template <class TypeTag>
class NavierStokesAnalyticProblem;
 
namespace Properties {
// Create new type tags
namespace TTag {
struct NavierStokesAnalytic { using InheritsFrom = std::tuple<NavierStokes, StaggeredFreeFlowModel>; };
} // end namespace TTag
 
// the fluid system
template<class TypeTag>
struct FluidSystem<TypeTag, TTag::NavierStokesAnalytic>
{
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using type = FluidSystems::OnePLiquid<Scalar, Components::Constant<1, Scalar> >;
};
 
// Set the grid type
template<class TypeTag>
struct Grid<TypeTag, TTag::NavierStokesAnalytic> { using type = Dune::YaspGrid<1>; };
 
// Set the problem property
template<class TypeTag>
struct Problem<TypeTag, TTag::NavierStokesAnalytic> { using type = Dumux::NavierStokesAnalyticProblem<TypeTag> ; };
 
template<class TypeTag>
struct EnableGridGeometryCache<TypeTag, TTag::NavierStokesAnalytic> { static constexpr bool value = true; };
 
template<class TypeTag>
struct EnableGridFluxVariablesCache<TypeTag, TTag::NavierStokesAnalytic> { static constexpr bool value = true; };
template<class TypeTag>
struct EnableGridVolumeVariablesCache<TypeTag, TTag::NavierStokesAnalytic> { static constexpr bool value = true; };
 
template<class TypeTag>
struct NormalizePressure<TypeTag, TTag::NavierStokesAnalytic> { static constexpr bool value = false; };
} // end namespace Properties
 
template <class TypeTag>
class NavierStokesAnalyticProblem : public NavierStokesProblem<TypeTag>
{
    using ParentType = NavierStokesProblem<TypeTag>;
 
    using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
    using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;
    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
 
    static constexpr auto dimWorld = GetPropType<TypeTag, Properties::GridView>::dimensionworld;
    using Element = typename GridGeometry::GridView::template Codim<0>::Entity;
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;
    using DimVector = GlobalPosition;
    using DimMatrix = Dune::FieldMatrix<Scalar, dimWorld, dimWorld>;
 
public:
    NavierStokesAnalyticProblem(std::shared_ptr<const GridGeometry> gridGeometry)
    : ParentType(gridGeometry), eps_(1e-6)
    {
        printL2Error_ = getParam<bool>("Problem.PrintL2Error");
        density_ = getParam<Scalar>("Component.LiquidDensity");
        kinematicViscosity_ = getParam<Scalar>("Component.LiquidKinematicViscosity");
        createAnalyticalSolution_();
    }
 
    // \{
 
    bool shouldWriteRestartFile() const
    {
        return false;
    }
 
    void printL2Error(const SolutionVector& curSol) const
    {
        if(printL2Error_)
        {
            using L2Error = NavierStokesTestL2Error<Scalar, ModelTraits, PrimaryVariables>;
            const auto l2error = L2Error::calculateL2Error(*this, curSol);
            const int numCellCenterDofs = this->gridGeometry().numCellCenterDofs();
            const int numFaceDofs = this->gridGeometry().numFaceDofs();
            std::cout << std::setprecision(8) << "** L2 error (abs/rel) for "
                    << std::setw(6) << numCellCenterDofs << " cc dofs and " << numFaceDofs << " face dofs (total: " << numCellCenterDofs + numFaceDofs << "): "
                    << std::scientific
                    << "L2(p) = " << l2error.first[Indices::pressureIdx] << " / " << l2error.second[Indices::pressureIdx]
                    << " , L2(vx) = " << l2error.first[Indices::velocityXIdx] << " / " << l2error.second[Indices::velocityXIdx]
                    << std::endl;
        }
    }
 
    Scalar temperature() const
    { return 298.0; }
 
    NumEqVector sourceAtPos(const GlobalPosition &globalPos) const
    {
        NumEqVector source(0.0);
 
        // mass balance - term div(rho*v)
        for (unsigned int dimIdx = 0; dimIdx < dimWorld; ++dimIdx)
        {
            source[Indices::conti0EqIdx] += dvdx(globalPos)[dimIdx][dimIdx];
        }
        source[Indices::conti0EqIdx] *= density_;
 
        // momentum balance
        for (unsigned int velIdx = 0; velIdx < dimWorld; ++velIdx)
        {
            for (unsigned int dimIdx = 0; dimIdx < dimWorld; ++dimIdx)
            {
                // inertia term
                if (this->enableInertiaTerms())
                  source[Indices::velocity(velIdx)] += density_ * dv2dx(globalPos)[velIdx][dimIdx];
 
                // viscous term (molecular)
                source[Indices::velocity(velIdx)] -= density_ * kinematicViscosity_* dvdx2(globalPos)[velIdx][dimIdx];
                static const bool enableUnsymmetrizedVelocityGradient = getParam<bool>("FreeFlow.EnableUnsymmetrizedVelocityGradient", false);
                if (!enableUnsymmetrizedVelocityGradient)
                    source[Indices::velocity(velIdx)] -= density_ * kinematicViscosity_* dvdx2(globalPos)[dimIdx][velIdx];
            }
            // pressure term
            source[Indices::velocity(velIdx)] += dpdx(globalPos)[velIdx];
 
            // gravity term
            static const bool enableGravity = getParam<bool>("Problem.EnableGravity");
            if (enableGravity)
            {
                source[Indices::velocity(velIdx)] -= density_ * this->gravity()[velIdx];
            }
        }
 
        return source;
    }
    // \}
    // \{
 
    BoundaryTypes boundaryTypesAtPos(const GlobalPosition& globalPos) const
    {
        BoundaryTypes values;
 
        // set Dirichlet values for the velocity everywhere
        values.setDirichlet(Indices::momentumXBalanceIdx);
 
        return values;
    }
 
    bool isDirichletCell(const Element& element,
                         const typename GridGeometry::LocalView& fvGeometry,
                         const typename GridGeometry::SubControlVolume& scv,
                         int pvIdx) const
    {
        // set a fixed pressure in all cells at the boundary
        for (const auto& scvf : scvfs(fvGeometry))
            if (scvf.boundary())
                return true;
 
        return false;
    }
 
    PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
    {
        // use the values of the analytical solution
        return analyticalSolution(globalPos);
    }
 
    PrimaryVariables analyticalSolution(const GlobalPosition& globalPos) const
    {
        PrimaryVariables values;
        values[Indices::pressureIdx] = p(globalPos);
        values[Indices::velocityXIdx] = v(globalPos);
        return values;
    }
 
    const DimVector v(const DimVector& globalPos) const
    {
        DimVector v(0.0);
        v[0] = 2.0 * globalPos[0] * globalPos[0] * globalPos[0];
        return v;
    }
 
    const DimMatrix dvdx(const DimVector& globalPos) const
    {
        DimMatrix dvdx(0.0);
        dvdx[0][0] = 6.0 * globalPos[0] * globalPos[0];
        return dvdx;
    }
 
    const DimMatrix dv2dx(const DimVector& globalPos) const
    {
        DimMatrix dv2dx;
        for (unsigned int velIdx = 0; velIdx < dimWorld; ++velIdx)
        {
            for (unsigned int dimIdx = 0; dimIdx < dimWorld; ++dimIdx)
            {
                dv2dx[velIdx][dimIdx] = dvdx(globalPos)[velIdx][dimIdx] * v(globalPos)[dimIdx]
                                        + dvdx(globalPos)[dimIdx][dimIdx] * v(globalPos)[velIdx];
            }
        }
        return dv2dx;
    }
 
    const DimMatrix dvdx2(const DimVector& globalPos) const
    {
        DimMatrix dvdx2(0.0);
        dvdx2[0][0] = 12.0 * globalPos[0];
        return dvdx2;
    }
 
    const Scalar p(const DimVector& globalPos) const
    { return 2.0 - 2.0 * globalPos[0]; }
 
    const DimVector dpdx(const DimVector& globalPos) const
    {
        DimVector dpdx(0.0);
        dpdx[0] = -2.0;
        return dpdx;
    }
 
    // \}
 
    // \{
 
    PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const
    {
        return analyticalSolution(globalPos);
    }
 
    auto& getAnalyticalPressureSolution() const
    {
        return analyticalPressure_;
    }
 
    auto& getAnalyticalVelocitySolution() const
    {
        return analyticalVelocity_;
    }
 
    auto& getAnalyticalVelocitySolutionOnFace() const
    {
        return analyticalVelocityOnFace_;
    }
 
private:
 
    void createAnalyticalSolution_()
    {
        analyticalPressure_.resize(this->gridGeometry().numCellCenterDofs());
        analyticalVelocity_.resize(this->gridGeometry().numCellCenterDofs());
        analyticalVelocityOnFace_.resize(this->gridGeometry().numFaceDofs());
 
        for (const auto& element : elements(this->gridGeometry().gridView()))
        {
            auto fvGeometry = localView(this->gridGeometry());
            fvGeometry.bindElement(element);
            for (auto&& scv : scvs(fvGeometry))
            {
                auto ccDofIdx = scv.dofIndex();
                auto ccDofPosition = scv.dofPosition();
                auto analyticalSolutionAtCc = analyticalSolution(ccDofPosition);
 
                // velocities on faces
                for (auto&& scvf : scvfs(fvGeometry))
                {
                    const auto faceDofIdx = scvf.dofIndex();
                    const auto faceDofPosition = scvf.center();
                    const auto dirIdx = scvf.directionIndex();
                    const auto analyticalSolutionAtFace = analyticalSolution(faceDofPosition);
                    analyticalVelocityOnFace_[faceDofIdx][dirIdx] = analyticalSolutionAtFace[Indices::velocity(dirIdx)];
                }
 
                analyticalPressure_[ccDofIdx] = analyticalSolutionAtCc[Indices::pressureIdx];
 
                for(int dirIdx = 0; dirIdx < ModelTraits::dim(); ++dirIdx)
                    analyticalVelocity_[ccDofIdx][dirIdx] = analyticalSolutionAtCc[Indices::velocity(dirIdx)];
            }
        }
     }
 
    Scalar eps_;
    bool printL2Error_;
    Scalar density_;
    Scalar kinematicViscosity_;
    std::vector<Scalar> analyticalPressure_;
    std::vector<GlobalPosition> analyticalVelocity_;
    std::vector<GlobalPosition> analyticalVelocityOnFace_;
};
} // end namespace Dumux
 
#endif