[swe] Add new viscous no-slip friction law for thin film flow

dumux/material/fluidmatrixinteractions/frictionlaws/viscousnoslip.hh

+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
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+ *                                                                           *
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+/*!
+ * \file
+ * \ingroup Fluidmatrixinteractions
+ * \copydoc Dumux::FrictionLawViscousNoSlip
+ */
+#ifndef DUMUX_MATERIAL_FLUIDMATRIX_FRICTIONLAW_VISCOUS_NOSLIP_HH
+#define DUMUX_MATERIAL_FLUIDMATRIX_FRICTIONLAW_VISCOUS_NOSLIP_HH
+
+#include <algorithm>
+#include <cmath>
+#include <dune/common/math.hh>
+
+#include <dumux/material/fluidmatrixinteractions/frictionlaws/frictionlaw.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup Fluidmatrixinteractions
+ * \brief Implementation of a viscous no-slip bottom friction law
+ *
+ * This assumes thin film flow with a parabolic velocity profile in depth
+ * (for the depth-averaged shallow water equations). The velocity profile
+ * and associated bottom shear stress can be derived from plane Poiseuille flow
+ * with a free surface boundary condition on top and a no-slip boundary condition
+ * on the bottom.
+ */
+
+template <typename VolumeVariables>
+class FrictionLawViscousNoSlip : public FrictionLaw<VolumeVariables>
+{
+    using Scalar = typename VolumeVariables::PrimaryVariables::value_type;
+public:
+    /*!
+     * \brief Compute the bottom shear stress.
+     *
+     * Compute the bottom shear stress due to bottom friction.
+     * The bottom shear stress is a projection of the shear stress tensor onto the bottom plane.
+     * It can therefore be represented by a (tangent) vector with two entries.
+     *
+     * \return shear stress in N/m^2. First entry is the x-component, the second the y-component.
+     */
+    Dune::FieldVector<Scalar, 2> bottomShearStress(const VolumeVariables& volVars) const final
+    {
+        // assume a parabolic velocity profile with no-slip BC on the bottom
+        // and zero stress condition on the free surface
+        // note that the velocity corresponds to the height-averaged velocity
+        Dune::FieldVector<Scalar, 2> shearStress(0.0);
+        shearStress[0] = volVars.viscosity()*volVars.velocity(0) * 3.0 / volVars.waterDepth();
+        shearStress[1] = volVars.viscosity()*volVars.velocity(1) * 3.0 / volVars.waterDepth();
+        return shearStress;
+    }
+};
+
+} // end namespace Dumux
+
+#endif