problem.hh

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/*!
 * \file
 *
 * \brief Isothermal NAPL infiltration problem: LNAPL contaminates
 *        the unsaturated and the saturated groundwater zone.
 */
#ifndef DUMUX_NAPLINFILTRATIONPROBLEM_3P_HH
#define DUMUX_NAPLINFILTRATIONPROBLEM_3P_HH

#include <dumux/porousmediumflow/3p/implicit/propertydefaults.hh>
#include <dumux/porousmediumflow/implicit/problem.hh>

#include <lecture/mm/naplinfiltration/h2oairnaplfluidsystem.hh>
#include <lecture/mm/naplinfiltration/spatialparams.hh>

namespace Dumux
{
template <class TypeTag>
class InfiltrationProblem;

namespace Properties
{
NEW_TYPE_TAG(InfiltrationProblem, INHERITS_FROM(BoxThreeP, InfiltrationSpatialParams));

// Set the grid type
SET_TYPE_PROP(InfiltrationProblem, Grid, Dune::YaspGrid<2>);

// Set the problem property
SET_TYPE_PROP(InfiltrationProblem, Problem, Dumux::InfiltrationProblem<TypeTag>);

// Set the fluid system
SET_TYPE_PROP(InfiltrationProblem,
              FluidSystem,
              FluidSystems::H2OAirNAPL<TypeTag, typename GET_PROP_TYPE(TypeTag, Scalar)>);

// Enable gravity?
SET_BOOL_PROP(InfiltrationProblem, ProblemEnableGravity, true);

// Write newton convergence?
SET_BOOL_PROP(InfiltrationProblem, NewtonWriteConvergence, false);

// Maximum tolerated relative error in the Newton method
SET_SCALAR_PROP(InfiltrationProblem, NewtonMaxRelativeShift, 1e-4);

// -1 backward differences, 0: central differences, +1: forward differences
SET_INT_PROP(InfiltrationProblem, ImplicitNumericDifferenceMethod, 1);
}

/*!
 * \ingroup ThreePThreeCBoxModel
 * \ingroup BoxTestProblems
 * \brief Isothermal NAPL infiltration problem: LNAPL contaminates
 *        the unsaturated and the saturated groundwater zone.
 *
 * The 2D domain of this test problem is 500 m long and 10 m deep, where
 * the lower part represents a slightly inclined groundwater table, and the
 * upper part is the vadose zone.
 * A LNAPL (Non-Aqueous Phase Liquid which is lighter than water) infiltrates
 * (modelled with a Neumann boundary condition) into the vadose zone. Upon
 * reaching the water table, it spreads (since lighter than water) and migrates
 * on top of the water table in the direction of the slope.
 * On its way through the vadose zone, it leaves a trace of residually trapped
 * immobile NAPL, which can in the following dissolve and evaporate slowly,
 * and eventually be transported by advection and diffusion.
 *
 * Left and right boundaries are constant head boundaries (Dirichlet),
 * Top and bottom are Neumann boundaries, all no-flow except for the small
 * infiltration zone in the upper left part.
 *
 * This problem uses the \ref ThreePThreeCModel or the \ref ThreePModel.
 *
 * This problem should typically be simulated for 30 days.
 * A good choice for the initial time step size is 60 s.
 * To adjust the simulation time it is necessary to edit the file test_naplfiltrationexercise.input
 *
 * To run the simulation execute the following line in shell:
 * <tt>./test_naplfiltrationexercise -ParameterFile test_naplfiltrationexercise.input</tt>
 *  */
template <class TypeTag >
class InfiltrationProblem : public ImplicitPorousMediaProblem<TypeTag>
{
    typedef ImplicitPorousMediaProblem<TypeTag> ParentType;

    typedef typename GET_PROP_TYPE(TypeTag, Scalar) Scalar;
    typedef typename GET_PROP_TYPE(TypeTag, GridView) GridView;

    // copy some indices for convenience
    typedef typename GET_PROP_TYPE(TypeTag, Indices) Indices;
    enum {
        pressureIdx = Indices::pressureIdx,
        switch1Idx = Indices::swIdx,
        switch2Idx = Indices::snIdx,

        contiWEqIdx = Indices::contiWEqIdx,
        contiNEqIdx = Indices::contiNEqIdx,
        contiGEqIdx = Indices::contiGEqIdx,

        // Grid and world dimension
        dim = GridView::dimension,
        dimWorld = GridView::dimensionworld
    };


    typedef typename GET_PROP_TYPE(TypeTag, PrimaryVariables) PrimaryVariables;
    typedef typename GET_PROP_TYPE(TypeTag, BoundaryTypes) BoundaryTypes;
    typedef typename GET_PROP_TYPE(TypeTag, TimeManager) TimeManager;

    typedef typename GridView::template Codim<0>::Entity Element;
    typedef typename GridView::template Codim<dim>::Entity Vertex;

    typedef typename GET_PROP_TYPE(TypeTag, FVElementGeometry) FVElementGeometry;
    typedef typename GET_PROP_TYPE(TypeTag, FluidSystem) FluidSystem;
    typedef typename GET_PROP_TYPE(TypeTag, MaterialLaw) MaterialLaw;
    typedef typename GET_PROP_TYPE(TypeTag, MaterialLawParams) MaterialLawParams;

    typedef Dune::FieldVector<Scalar, dimWorld> GlobalPosition;

public:
    /*!
     * \brief The constructor
     *
     * \param timeManager The time manager
     * \param gridView The grid view
     */
    InfiltrationProblem(TimeManager &timeManager, const GridView &gridView)
        : ParentType(timeManager, gridView), eps_(1e-5)
    {
        temperature_ = 273.15 + 10.0; // -> 10 degrees Celsius

        episodeLength_ = GET_RUNTIME_PARAM_FROM_GROUP(TypeTag, Scalar, TimeManager, EpisodeLength);
        this->timeManager().startNextEpisode(episodeLength_);

        FluidSystem::init(/*tempMin=*/temperature_ - 1,
                          /*tempMax=*/temperature_ + 1,
                          /*nTemp=*/3,
                          /*pressMin=*/0.8*1e5,
                          /*pressMax=*/3*1e5,
                          /*nPress=*/200);
    }

    /*!
     * \name Problem parameters
     */
    // \{

    /*!
     * \brief The problem name.
     *
     * This is used as a prefix for files generated by the simulation.
     */
    std::string name() const
    { return "infiltration3p"; }

    /*!
     * \brief Returns the temperature within the domain.
     *
     * This problem assumes a temperature of 10 degrees Celsius.
     */
    Scalar temperature() const
    {
        return temperature_;
    };

    void sourceAtPos(PrimaryVariables &values,
                     const GlobalPosition &globalPos) const
    {
        values = 0;
    }

    // \}

    /*!
     * \name Boundary conditions
     */
    // \{

    /*!
     * \brief Specifies which kind of boundary condition should be
     *        used for which equation on a given boundary segment.
     *
     * \param values The boundary types for the conservation equations
     * \param globalPos The position of the finite volume in global coordinates
     */
    void boundaryTypesAtPos(BoundaryTypes &values,
                            const GlobalPosition &globalPos) const
    {
        if(globalPos[0] > this->bBoxMax()[0] - eps_)
            values.setAllDirichlet();
        else if(globalPos[0] < this->bBoxMin()[0] + eps_)
            values.setAllDirichlet();
        else
            values.setAllNeumann();
    }

    /*!
     * \brief Evaluate the boundary conditions for a dirichlet
     *        control volume.
     *
     * \param values The dirichlet values for the primary variables
     * \param globalPos The position of the center of the finite volume
     *            for which the dirichlet condition ought to be
     *            set in global coordinates
     *
     * For this method, the \a values parameter stores primary variables.
     */
    void dirichletAtPos(PrimaryVariables &values,
                        const GlobalPosition &globalPos) const
    {
        initial_(values, globalPos);
    }

    /*!
     * \brief Evaluate the boundary conditions for a neumann
     *        boundary segment.
     *
     * \param values The neumann values for the conservation equations in units of
     *                 \f$ [ \textnormal{unit of conserved quantity} / (m^2 \cdot s )] \f$
     * \param globalPos The position of the boundary face's integration point in global coordinates
     *
     * For this method, the \a values parameter stores the mass flux
     * in normal direction of each phase. Negative values mean influx.
     */
    void neumannAtPos(PrimaryVariables &values,
                      const GlobalPosition &globalPos) const
    {
        values = 0;

        // negative values for injection
        if (this->timeManager().time() < 2592000)
        {
            if (globalPos[0] < 175.0 + eps_
                && globalPos[0] > 150.0 - eps_
                && globalPos[1] > this->bBoxMax()[1] - eps_) // upper boundary
            {
                values[contiWEqIdx] = 0.0;
                // mole flux conversion via M(mesit.) = 0,120 kg/mol --> 1.2e-4  kg/(s*m)
                values[contiNEqIdx] = -0.001*0.12; // 3p needs a mass fraction
                values[contiGEqIdx] = 0.0;
            }
        }
    }

    // \}

    /*!
     * \name Volume terms
     */
    // \{

    /*!
     * \brief Evaluate the initial value for a control volume.
     *
     * \param values The dirichlet values for the primary variables
     * \param globalPos The position of the center of the finite volume
     *            for which the initial values ought to be
     *            set (in global coordinates)
     *
     * For this method, the \a values parameter stores primary variables.
     */
    void initialAtPos(PrimaryVariables &values,
                      const GlobalPosition &globalPos) const
    {
        initial_(values, globalPos);
    }

    bool shouldWriteOutput() const
    {
    return this->timeManager().timeStepIndex() == 0 ||
           this->timeManager().episodeWillBeFinished() ||
           this->timeManager().willBeFinished();
    }

    void episodeEnd()
    {
        this->timeManager().startNextEpisode(episodeLength_);
    }

private:
    // internal method for the initial condition (reused for the
    // dirichlet conditions!)
    void initial_(PrimaryVariables &values,
                  const GlobalPosition &globalPos) const
    {
        const auto& materialLawParams = this->spatialParams().materialLawParams();
        const Scalar swr = materialLawParams.swr();
        const Scalar sgr = materialLawParams.sgr();

        if(globalPos[1] >= -1e-3*globalPos[0] + 5)
        {
            const Scalar pc = std::max(0.0, 9.81*1000.0*(globalPos[1] + 5e-4*globalPos[0] - 5));
            const Scalar sw = std::min(1.0-sgr, std::max(swr, invertPcGW_(pc, materialLawParams)));

            values[pressureIdx] = 1.0e5;
            values[switch1Idx] = sw;
            values[switch2Idx] = 0.0;
        }
        else
        {
            values[pressureIdx] = 1.0e5 + 9.81*1000.0*(5 - 5.0e-4*globalPos[0] - globalPos[1]);
            values[switch1Idx] = 1.0 - sgr;
            values[switch2Idx] = 0.0;
        }
    }

    static Scalar invertPcGW_(const Scalar pcIn,
                              const MaterialLawParams &pcParams)
    {
        Scalar lower(0.0);
        Scalar upper(1.0);
        const unsigned int maxIterations = 25;
        const Scalar bisLimit = 1.0;

        Scalar sw, pcGW;
        for (unsigned int k = 1; k <= maxIterations; k++)
        {
            sw = 0.5*(upper + lower);
            pcGW = MaterialLaw::pcgw(pcParams, sw);
            const Scalar delta = std::abs(pcGW - pcIn);
            if (delta < bisLimit)
                return sw;

            if (k == maxIterations)
                return sw;

            if (pcGW > pcIn)
                lower = sw;
            else
                upper = sw;
        }
        return sw;
    }

    Scalar temperature_;
    const Scalar eps_;
    Scalar episodeLength_;
};
} //end namespace

#endif