78 const typename FVElementGeometry::GridGeometry::GridView::template Codim<0>::Entity& element,
79 const FVElementGeometry& fvGeometry,
80 const ElementVolumeVariables& elemVolVars,
81 const typename FVElementGeometry::SubControlVolumeFace& scvf)
83 using Scalar =
typename NumEqVector::value_type;
84 using FluidSystem =
typename ElementVolumeVariables::VolumeVariables::FluidSystem;
89 const auto& insideVolVars = elemVolVars[scvf.insideScvIdx()];
90 const auto& outsideVolVars = elemVolVars[scvf.outsideScvIdx()];
92 const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
93 const auto& outsideScv = fvGeometry.scv(scvf.outsideScvIdx());
95 const auto gradVelocity = [&]()
98 const auto velocityXLeft = insideVolVars.velocity(0);
99 const auto velocityYLeft = insideVolVars.velocity(1);
100 const auto velocityXRight = outsideVolVars.velocity(0);
101 const auto velocityYRight = outsideVolVars.velocity(1);
105 const auto& cellCenterToCellCenter = outsideScv.center() - insideScv.center();
106 const auto distance = cellCenterToCellCenter.two_norm();
107 const auto&
unitNormal = scvf.unitOuterNormal();
109 return std::array<Scalar, 2>{
110 (velocityXRight-velocityXLeft)*direction/
distance,
111 (velocityYRight-velocityYLeft)*direction/
distance
116 const auto waterDepthLeft = insideVolVars.waterDepth();
117 const auto waterDepthRight = outsideVolVars.waterDepth();
118 const auto averageDepth = 2.0*(waterDepthLeft*waterDepthRight)/(waterDepthLeft + waterDepthRight);
120 const Scalar effectiveKinematicViscosity = [&]()
126 problem.paramGroup(),
"ShallowWater.TurbulentViscosity", insideVolVars.viscosity()/insideVolVars.density()
131 problem.paramGroup(),
"ShallowWater.UseMixingLengthTurbulenceModel",
false
135 if (!useMixingLengthTurbulenceModel)
136 return backgroundKinematicViscosity;
138 using SpatialParams =
typename Problem::SpatialParams;
139 using E =
typename FVElementGeometry::GridGeometry::GridView::template Codim<0>::Entity;
140 using SCV =
typename FVElementGeometry::SubControlVolume;
141 if constexpr (!Detail::implementsFrictionLaw<SpatialParams, E, SCV>())
142 DUNE_THROW(Dune::IOError,
"Mixing length turbulence model enabled but spatial parameters do not implement the frictionLaw interface!");
148 static const auto turbConstV =
getParamFromGroup<Scalar>(problem.paramGroup(),
"ShallowWater.VerticalCoefficientOfMixingLengthModel", 1.0);
149 static const auto turbConstH =
getParamFromGroup<Scalar>(problem.paramGroup(),
"ShallowWater.HorizontalCoefficientOfMixingLengthModel", 0.1);
157 constexpr Scalar kappa = 0.41;
159 const Scalar ustar = [&]()
163 const auto& bottomShearStressInside = problem.spatialParams().frictionLaw(element, insideScv).bottomShearStress(insideVolVars);
164 const auto& bottomShearStressOutside = problem.spatialParams().frictionLaw(element, outsideScv).bottomShearStress(outsideVolVars);
165 const auto bottomShearStressInsideMag = bottomShearStressInside.two_norm();
166 const auto bottomShearStressOutsideMag = bottomShearStressOutside.two_norm();
170 const auto averageBottomShearStress = 2.0*(bottomShearStressInsideMag*bottomShearStressOutsideMag)
171 / max(1.0e-8,bottomShearStressInsideMag + bottomShearStressOutsideMag);
175 static_assert(!FluidSystem::isCompressible(0),
176 "The shallow water model assumes incompressible fluids"
180 return sqrt(averageBottomShearStress/insideVolVars.density());
183 const auto turbViscosityV = turbConstV * (kappa/6.0) * ustar * averageDepth;
210 const auto [gradU, gradV] = gradVelocity;
211 const auto mixingLengthSquared = turbConstH * turbConstH * averageDepth * averageDepth;
212 const auto turbViscosityH = mixingLengthSquared * sqrt(2.0*gradU*gradU + 2.0*gradV*gradV);
215 return backgroundKinematicViscosity + sqrt(turbViscosityV*turbViscosityV + turbViscosityH*turbViscosityH);
222 const auto freeSurfaceInside = insideVolVars.waterDepth() + insideVolVars.bedSurface();
223 const auto freeSurfaceOutside = outsideVolVars.waterDepth() + outsideVolVars.bedSurface();
224 const auto interfaceWaterDepth = max(min(freeSurfaceInside , freeSurfaceOutside) - max(insideVolVars.bedSurface(),outsideVolVars.bedSurface()),0.0);
225 const auto& [gradU, gradV] = gradVelocity;
226 const auto uViscousFlux = effectiveKinematicViscosity * interfaceWaterDepth * gradU;
227 const auto vViscousFlux = effectiveKinematicViscosity * interfaceWaterDepth * gradV;
230 localFlux[1] = -uViscousFlux * scvf.area();
231 localFlux[2] = -vViscousFlux * scvf.area();