facetensoraverage.hh

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#ifndef DUMUX_FACE_TENSOR_AVERAGE_HH
#define DUMUX_FACE_TENSOR_AVERAGE_HH
 
#include <dune/common/fmatrix.hh>
#include <dumux/common/math.hh>
 
namespace Dumux {
 
template <class Scalar, int dim>
Scalar faceTensorAverage(const Scalar T1,
                         const Scalar T2,
                         const Dune::FieldVector<Scalar, dim>& normal)
{ return Dumux::harmonicMean(T1, T2); }
 
template <class Scalar, int dim>
Dune::FieldMatrix<Scalar, dim> faceTensorAverage(const Dune::FieldMatrix<Scalar, dim>& T1,
                                                 const Dune::FieldMatrix<Scalar, dim>& T2,
                                                 const Dune::FieldVector<Scalar, dim>& normal)
{
    // determine nT*k*n
    Dune::FieldVector<Scalar, dim> tmp;
    Dune::FieldVector<Scalar, dim> tmp2;
    T1.mv(normal, tmp);
    T2.mv(normal, tmp2);
    const Scalar alpha1 = tmp*normal;
    const Scalar alpha2 = tmp2*normal;
 
    const Scalar alphaHarmonic = Dumux::harmonicMean(alpha1, alpha2);
    const Scalar alphaAverage = 0.5*(alpha1 + alpha2);
 
    Dune::FieldMatrix<Scalar, dim> T(0.0);
    for (int i = 0; i < dim; ++i)
    {
        for (int j = 0; j < dim; ++j)
        {
            T[i][j] += 0.5*(T1[i][j] + T2[i][j]);
            if (i == j)
                T[i][j] += alphaHarmonic - alphaAverage;
        }
    }
 
    return T;
}
 
} // end namespace Dumux
 
#endif