problem.hh

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

#include <dumux/common/properties.hh>
#include <dumux/common/parameters.hh>

#include <dumux/porousmediumflow/problem.hh>


namespace Dumux
{
/*!
 * \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 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 naplinfiltrationexercise.input
 *
 * To run the simulation execute the following line in shell:
 * <tt>./naplinfiltrationexercise -parameterFile naplinfiltrationexercise.input</tt>
 *  */
template <class TypeTag >
class InfiltrationThreePProblem : public PorousMediumFlowProblem<TypeTag>
{
    using ParentType = PorousMediumFlowProblem<TypeTag>;

    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView;
    using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;

    enum {
        pressureIdx = Indices::pressureIdx,
        swIdx = Indices::swIdx,
        snIdx = Indices::snIdx,

        // world dimension
        dimWorld = GridView::dimensionworld
    };

    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
    using NumEqVector = GetPropType<TypeTag, Properties::NumEqVector>;
    using BoundaryTypes = GetPropType<TypeTag, Properties::BoundaryTypes>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    using FVGridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;

    using Element = typename GridView::template Codim<0>::Entity;
    using GlobalPosition = typename Element::Geometry::GlobalCoordinate;

public:
    /*!
     * \brief The constructor
     *
     */
    InfiltrationThreePProblem(std::shared_ptr<const FVGridGeometry> fvGridGeometry)
    : ParentType(fvGridGeometry)
    {
        temperature_ = 273.15 + 10.0; // -> 10 degrees Celsius
        FluidSystem::init(282.15, 284.15, 3, 8e4, 3e5, 200);

        name_ = getParam<std::string>("Problem.Name");

        this->spatialParams().plotMaterialLaw();
        time_ = 0.0;
    }

    /*!
     * \name Problem parameters
     */
    // \{
    void setTime(Scalar time)
    { time_ = time; }

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

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

    // \}

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

    /*!
     * \brief Specifies which kind of boundary condition should be
     *        used for which equation on a given boundary segment.
     *
     * \param globalPos The position for which the bc type should be evaluated
     */
    BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const
    {
        BoundaryTypes values;

        if(globalPos[0] > this->gridGeometry().bBoxMax()[0] - eps_
           || globalPos[0] < this->gridGeometry().bBoxMin()[0] + eps_)
            values.setAllDirichlet();
        else
            values.setAllNeumann();

        return values;
    }

    /*!
     * \brief Evaluate the boundary conditions for a dirichlet
     *        boundary segment.
     *
     * \param values The dirichlet values for the primary variables
     * \param globalPos The position for which the bc type should be evaluated
     *
     * For this method, the \a values parameter stores primary variables.
     */
    PrimaryVariables dirichletAtPos(const GlobalPosition &globalPos) const
    {
        return initial_(globalPos);
    }
    /*!
     * \brief Evaluate the boundary conditions for a neumann
     *        boundary segment.
     *
     * \param globalPos The position of the integration point of the boundary segment.
     *
     * For this method, the \a values parameter stores the mass flux
     * in normal direction of each phase. Negative values mean influx.
     */
    NumEqVector neumannAtPos(const GlobalPosition &globalPos) const
    {
        NumEqVector values(0.0);

        // negative values for injection
        if (time_ < 2592000.0 - eps_)
        {
            if ((globalPos[0] < 175.0 + eps_) && (globalPos[0] > 150.0 - eps_)
                 && (globalPos[1] > this->gridGeometry().bBoxMax()[1] - eps_))
            {
                // mol fluxes, convert with M(Mesit.)=0,120 kg/mol --> 1.2e-4  kg/(sm)
                values[Indices::conti0EqIdx + FluidSystem::nCompIdx] = -0.001*0.12;
            }
        }

        return values;
    }

    // \}

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

    /*!
     * \brief Evaluate the initial value for a control volume.
     *
     * \param globalPos The position for which the initial condition should be evaluated
     *
     * For this method, the \a values parameter stores primary
     * variables.
     */
    PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const
    {
        return initial_(globalPos);
    }

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



private:
    // internal method for the initial condition (reused for the
    // dirichlet conditions!)
    PrimaryVariables initial_(const GlobalPosition &globalPos) const
    {
        PrimaryVariables values(0.0);

        Scalar y = globalPos[1];
        Scalar x = globalPos[0];

        const auto& materialLawParams = this->spatialParams().materialLawParamsAtPos(globalPos);
        Scalar swr = materialLawParams.swr();
        Scalar sgr = materialLawParams.sgr();

        if(y > (-1e-3*x+5) - eps_)
        {
            Scalar pc = 9.81 * 1000.0 * (y - (-5e-4*x+5));
            if (pc < 0.0) pc = 0.0;

            Scalar sw = invertPcgw_(pc, this->spatialParams().materialLawParamsAtPos(globalPos));
            if(sw < swr) sw = swr;
            if(sw > 1.-sgr) sw = 1.-sgr;

            values[pressureIdx] = 1e5;
            values[swIdx] = sw;
            values[snIdx] = 0.;
        }else
        {
            values[pressureIdx] = 1e5 + 9.81 * 1000.0 * ((-5e-4*x+5) - y);
            values[swIdx] = 1.-sgr;
            values[snIdx] = 0.;
        }

        return values;
    }

    // small solver inverting the pc curve
    template<class MaterialLawParams>
    static Scalar invertPcgw_(Scalar pcIn, const MaterialLawParams &pcParams)
    {
        using MaterialLaw = typename ParentType::SpatialParams::MaterialLaw;
        Scalar lower(0.0);
        Scalar upper(1.0);
        const unsigned int maxIter = 25;
        const Scalar bisLimit = 1.0;

        Scalar sw, pcgw;
        for (unsigned int k = 1; k <= maxIter; 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 == maxIter)
                return sw;

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

    Scalar temperature_;
    static constexpr Scalar eps_ = 1e-6;
    std::string name_;
    Scalar time_;
};

} // end namespace Dumux

#endif