flux/porenetwork/fourierslaw.hh

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#ifndef DUMUX_FLUX_PNM_FOURIERS_LAW_HH
#define DUMUX_FLUX_PNM_FOURIERS_LAW_HH
 
#include <dumux/common/math.hh>
#include <dumux/flux/referencesystemformulation.hh>
#include <type_traits>
 
namespace Dumux::PoreNetwork {
 
namespace Detail {
 
struct NoDiffusionType {};
 
} // end namespace Detail

template<class MolecularDiffusionType = Detail::NoDiffusionType>
struct PNMFouriersLaw
{
 
    template<class Problem, class Element, class FVElementGeometry,
             class ElementVolumeVariables, class ElementFluxVariablesCache>
    static auto flux(const Problem& problem,
                     const Element& element,
                     const FVElementGeometry& fvGeometry,
                     const ElementVolumeVariables& elemVolVars,
                     const typename FVElementGeometry::SubControlVolumeFace& scvf,
                     const ElementFluxVariablesCache& elemFluxVarsCache)
    {
        const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
        const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
        const auto& insideVolVars = elemVolVars[insideScv];
        const auto& outsideVolVars = elemVolVars[outsideScv];
        const auto& fluxVarsCache = elemFluxVarsCache[scvf];
 
        static constexpr auto numPhases = ElementVolumeVariables::VolumeVariables::numFluidPhases();
        using Scalar = typename ElementVolumeVariables::VolumeVariables::PrimaryVariables::value_type;
        Scalar heatflux = 0;
 
        for (int phaseIdx = 0; phaseIdx < numPhases; phaseIdx++)
        {
            auto insideThermalConducitivity = insideVolVars.fluidThermalConductivity(phaseIdx);
            auto outsideThermalConducitivity = outsideVolVars.fluidThermalConductivity(phaseIdx);
 
            auto thermalConductivity = Dumux::harmonicMean(insideThermalConducitivity, outsideThermalConducitivity);
            auto area = fluxVarsCache.throatCrossSectionalArea(phaseIdx);
 
            // calculate the temperature gradient
            const Scalar deltaT = insideVolVars.temperature() - outsideVolVars.temperature();
            const Scalar gradT = deltaT/fluxVarsCache.throatLength();
 
            heatflux += thermalConductivity*gradT*area;
 
            if constexpr (!std::is_same_v<MolecularDiffusionType, Detail::NoDiffusionType>)
                heatflux += componentEnthalpyFlux_(problem, element, fvGeometry, elemVolVars, scvf, elemFluxVarsCache, phaseIdx);
        }
 
        return heatflux;
    }
 
private:
    template<class Problem, class Element, class FVElementGeometry,
             class ElementVolumeVariables, class ElementFluxVariablesCache>
    static auto componentEnthalpyFlux_(const Problem& problem,
                                       const Element& element,
                                       const FVElementGeometry& fvGeometry,
                                       const ElementVolumeVariables& elemVolVars,
                                       const typename FVElementGeometry::SubControlVolumeFace& scvf,
                                       const ElementFluxVariablesCache& elemFluxVarsCache,
                                       const int phaseIdx)
    {
        using Scalar = typename ElementVolumeVariables::VolumeVariables::PrimaryVariables::value_type;
        Scalar heatflux = 0.0;
        using FluidSystem = typename ElementVolumeVariables::VolumeVariables::FluidSystem;
        const auto diffusiveFlux = MolecularDiffusionType::flux(problem, element, fvGeometry, elemVolVars, scvf, phaseIdx, elemFluxVarsCache);
        for (int compIdx = 0; compIdx < ElementVolumeVariables::VolumeVariables::numFluidComponents(); ++compIdx)
        {
            const bool insideIsUpstream = diffusiveFlux[compIdx] > 0.0;
            const auto& upstreamVolVars = insideIsUpstream ? elemVolVars[scvf.insideScvIdx()] : elemVolVars[scvf.outsideScvIdx()];
            const Scalar componentEnthalpy = FluidSystem::componentEnthalpy(upstreamVolVars.fluidState(), phaseIdx, compIdx);
 
            if (MolecularDiffusionType::referenceSystemFormulation() == ReferenceSystemFormulation::massAveraged)
                heatflux += diffusiveFlux[compIdx] * componentEnthalpy;
            else
                heatflux += diffusiveFlux[compIdx] * FluidSystem::molarMass(compIdx) * componentEnthalpy;
        }
 
        return heatflux;
    }
};
 
} // end namespace Dumux::PoreNetwork
 
#endif