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| 1 | // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- | ||
| 2 | // vi: set et ts=4 sw=4 sts=4: | ||
| 3 | // | ||
| 4 | // SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | |||
| 8 | #ifndef DUMUX_POISEUILLE_FLOW_VERTICAL_TEST_PROBLEM_HH | ||
| 9 | #define DUMUX_POISEUILLE_FLOW_VERTICAL_TEST_PROBLEM_HH | ||
| 10 | |||
| 11 | #include <algorithm> | ||
| 12 | #include <cctype> | ||
| 13 | |||
| 14 | #include <dumux/common/properties.hh> | ||
| 15 | #include <dumux/common/parameters.hh> | ||
| 16 | #include <dumux/common/numeqvector.hh> | ||
| 17 | |||
| 18 | #include <dumux/freeflow/shallowwater/problem.hh> | ||
| 19 | #include <dumux/freeflow/shallowwater/boundaryfluxes.hh> | ||
| 20 | |||
| 21 | namespace Dumux { | ||
| 22 | |||
| 23 | /*! | ||
| 24 | * \ingroup ShallowWaterTests | ||
| 25 | * \brief A simple test for the 2D flow in a channel with viscous bottom friction (plane Poiseuille flow). | ||
| 26 | * In comparison to the other Poiseuille flow test, here we assume a rectangular channel with zero friction walls | ||
| 27 | * but viscous friction due to bottom shear stress. | ||
| 28 | * The result is a parabolic velocity profile \f$ U(z) \f$ over the height: | ||
| 29 | * \f[ | ||
| 30 | * U(z) = 3u(z/h - 0.5(z/h)^2) | ||
| 31 | * \f] | ||
| 32 | * bottom shear stress | ||
| 33 | * \f[ | ||
| 34 | * \tau = -\mu 3u/h | ||
| 35 | * \f] | ||
| 36 | * and mean velocity | ||
| 37 | * \f[ | ||
| 38 | * u = \frac{1}{3} \frac{h^2 \rho g S}{\mu} | ||
| 39 | * \f] | ||
| 40 | * where \f$ S \f$ denotes the bed slope in m/m. | ||
| 41 | * Therefore, in difference to the other test, the heigh-averaged velocity is constant over the channel width | ||
| 42 | * and to model the bottom surface, we need to include the effect of the bottom shear stress. | ||
| 43 | * This problem uses the \ref ShallowWaterModel | ||
| 44 | */ | ||
| 45 | template<class TypeTag> | ||
| 46 | class PoiseuilleFlowProblem | ||
| 47 | : public ShallowWaterProblem<TypeTag> | ||
| 48 | { | ||
| 49 | using ParentType = ShallowWaterProblem<TypeTag>; | ||
| 50 | using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; | ||
| 51 | using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>; | ||
| 52 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 53 | using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices; | ||
| 54 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 55 | using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView; | ||
| 56 | using GridVariables = GetPropType<TypeTag, Properties::GridVariables>; | ||
| 57 | using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView; | ||
| 58 | using VolumeVariables = typename ElementVolumeVariables::VolumeVariables; | ||
| 59 | using FVElementGeometry = typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView; | ||
| 60 | using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace; | ||
| 61 | using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView; | ||
| 62 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 63 | using GlobalPosition = typename Element::Geometry::GlobalCoordinate; | ||
| 64 | using NumEqVector = Dumux::NumEqVector<PrimaryVariables>; | ||
| 65 | using NeumannFluxes = NumEqVector; | ||
| 66 | using SubControlVolume = typename FVElementGeometry::SubControlVolume; | ||
| 67 | using FluidSystem = typename VolumeVariables::FluidSystem; | ||
| 68 | |||
| 69 | public: | ||
| 70 | 1 | PoiseuilleFlowProblem(std::shared_ptr<const GridGeometry> gridGeometry) | |
| 71 |
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3 | : ParentType(gridGeometry) |
| 72 | { | ||
| 73 | // assume box grid with flow in x-direction driven by gravity | ||
| 74 |
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6 | channelWidth_ = this->gridGeometry().bBoxMax()[1] - this->gridGeometry().bBoxMin()[1]; |
| 75 |
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1 | name_ = getParam<std::string>("Problem.Name"); |
| 76 |
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1 | bedSlope_ = getParam<Scalar>("Problem.BedSlope"); |
| 77 |
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1 | waterDepthBoundary_ = getParam<Scalar>("Problem.WaterDepth"); |
| 78 |
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1 | dynamicViscosity_ = FluidSystem::viscosity(293.15, 1e5); |
| 79 | |||
| 80 |
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2 | exactWaterDepth_.resize(gridGeometry->numDofs(), 0.0); |
| 81 |
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2 | exactVelocityX_.resize(gridGeometry->numDofs(), 0.0); |
| 82 |
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2 | exactVelocityY_.resize(gridGeometry->numDofs(), 0.0); |
| 83 | 1 | } | |
| 84 | |||
| 85 | const std::string& name() const | ||
| 86 |
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1 | { return name_; } |
| 87 | |||
| 88 | /*! | ||
| 89 | * \brief Specifies which kind of boundary condition should be | ||
| 90 | * used for which equation on a given boundary segment. | ||
| 91 | * | ||
| 92 | * \param globalPos The position for which the boundary type is set | ||
| 93 | */ | ||
| 94 | ✗ | BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const | |
| 95 | { | ||
| 96 | 440 | BoundaryTypes bcTypes; | |
| 97 |
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440 | bcTypes.setAllNeumann(); |
| 98 | ✗ | return bcTypes; | |
| 99 | } | ||
| 100 | |||
| 101 | /*! | ||
| 102 | * \brief Specifies the neumann boundary | ||
| 103 | * | ||
| 104 | * We need the Riemann invariants to compute the values depending of the boundary type. | ||
| 105 | * Since we use a weak imposition we do not have a dirichlet value. We impose fluxes | ||
| 106 | * based on q, h, etc. computed with the Riemann invariants | ||
| 107 | */ | ||
| 108 | 352 | NeumannFluxes neumann(const Element& element, | |
| 109 | const FVElementGeometry& fvGeometry, | ||
| 110 | const ElementVolumeVariables& elemVolVars, | ||
| 111 | const ElementFluxVariablesCache& elemFluxVarsCache, | ||
| 112 | const SubControlVolumeFace& scvf) const | ||
| 113 | { | ||
| 114 | 352 | NeumannFluxes values(0.0); | |
| 115 | |||
| 116 | 352 | const auto& globalPos = scvf.ipGlobal(); | |
| 117 | 704 | const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx()); | |
| 118 | 352 | const auto& insideVolVars = elemVolVars[insideScv]; | |
| 119 |
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352 | const auto& unitNormal = scvf.unitOuterNormal(); |
| 120 |
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352 | const auto gravity = this->spatialParams().gravity(globalPos); |
| 121 | std::array<Scalar, 3> boundaryStateVariables; | ||
| 122 | |||
| 123 |
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1408 | if (globalPos[1] > this->gridGeometry().bBoxMax()[1] - eps_ |
| 124 |
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352 | || globalPos[1] < this->gridGeometry().bBoxMin()[1] + eps_) |
| 125 | { | ||
| 126 | // full slip for tangential part and reflection (no-flow) for normal part | ||
| 127 | 1280 | const Scalar insideVelocityNormalWall = insideVolVars.velocity(0)*unitNormal[0] + insideVolVars.velocity(1)*unitNormal[1]; | |
| 128 | 1280 | const Scalar insideVelocityTangentWall = -insideVolVars.velocity(0)*unitNormal[1] + insideVolVars.velocity(1)*unitNormal[0]; | |
| 129 | 320 | const Scalar outsideVelocityNormalWall = -insideVelocityNormalWall; | |
| 130 | 320 | const Scalar outsideVelocityTangentWall = insideVelocityTangentWall; | |
| 131 | 640 | const Scalar outsideVelocityXWall = outsideVelocityNormalWall*unitNormal[0] - outsideVelocityTangentWall*unitNormal[1]; | |
| 132 | 640 | const Scalar outsideVelocityYWall = outsideVelocityNormalWall*unitNormal[1] + outsideVelocityTangentWall*unitNormal[0]; | |
| 133 | 640 | boundaryStateVariables = { insideVolVars.waterDepth(), outsideVelocityXWall, outsideVelocityYWall }; | |
| 134 | } | ||
| 135 | else | ||
| 136 | { | ||
| 137 | // for inlet and outlet, the same water depth is prescribed | ||
| 138 | 96 | boundaryStateVariables = ShallowWater::fixedWaterDepthBoundary( | |
| 139 | 32 | waterDepthBoundary_, | |
| 140 | insideVolVars.waterDepth(), insideVolVars.velocity(0), insideVolVars.velocity(1), | ||
| 141 | gravity, unitNormal | ||
| 142 | ); | ||
| 143 | } | ||
| 144 | |||
| 145 | 352 | auto riemannFlux = ShallowWater::riemannProblem( | |
| 146 | 704 | insideVolVars.waterDepth(), boundaryStateVariables[0], | |
| 147 | 704 | insideVolVars.velocity(0), boundaryStateVariables[1], | |
| 148 | 704 | insideVolVars.velocity(1), boundaryStateVariables[2], | |
| 149 | insideVolVars.bedSurface(), insideVolVars.bedSurface(), | ||
| 150 | gravity, unitNormal | ||
| 151 | ); | ||
| 152 | |||
| 153 | 1056 | values[Indices::massBalanceIdx] = riemannFlux[0]; | |
| 154 | 1056 | values[Indices::velocityXIdx] = riemannFlux[1]; | |
| 155 | 1056 | values[Indices::velocityYIdx] = riemannFlux[2]; | |
| 156 | |||
| 157 | // zero viscous part of the flux since we assume full slip on the walls | ||
| 158 | |||
| 159 | 352 | return values; | |
| 160 | } | ||
| 161 | |||
| 162 | // bottom friction source | ||
| 163 | 320 | NumEqVector source(const Element &element, | |
| 164 | const FVElementGeometry& fvGeometry, | ||
| 165 | const ElementVolumeVariables& elemVolVars, | ||
| 166 | const SubControlVolume& scv) const | ||
| 167 | { | ||
| 168 | 320 | NumEqVector bottomFrictionSource(0.0); | |
| 169 | |||
| 170 | 320 | const auto& volVars = elemVolVars[scv]; | |
| 171 | 320 | Dune::FieldVector<Scalar, 2> bottomShearStress = | |
| 172 | 960 | this->spatialParams().frictionLaw(element, scv).bottomShearStress(volVars); | |
| 173 | |||
| 174 | 640 | bottomFrictionSource[0] = 0.0; | |
| 175 | 1280 | bottomFrictionSource[1] = -bottomShearStress[0] / volVars.density(); | |
| 176 | 1280 | bottomFrictionSource[2] = -bottomShearStress[1] / volVars.density(); | |
| 177 | |||
| 178 | 320 | return bottomFrictionSource; | |
| 179 | } | ||
| 180 | |||
| 181 | // Set initial sol to the exact solution | ||
| 182 | ✗ | PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const | |
| 183 | { | ||
| 184 | 80 | return exactSol_(globalPos); | |
| 185 | }; | ||
| 186 | |||
| 187 | //! Update the analytical solution | ||
| 188 | 1 | void updateAnalyticalSolution() | |
| 189 | { | ||
| 190 |
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83 | for (const auto& element : elements(this->gridGeometry().gridView())) |
| 191 | { | ||
| 192 | 120 | const auto eIdx = this->gridGeometry().elementMapper().index(element); | |
| 193 | 40 | const auto& globalPos = element.geometry().center(); | |
| 194 | 80 | const auto sol = exactSol_(globalPos); | |
| 195 | 120 | exactWaterDepth_[eIdx] = sol[Indices::waterdepthIdx]; | |
| 196 | 120 | exactVelocityX_[eIdx] = sol[Indices::velocityXIdx]; | |
| 197 | 120 | exactVelocityY_[eIdx] = sol[Indices::velocityYIdx]; | |
| 198 | } | ||
| 199 | 1 | } | |
| 200 | |||
| 201 | //! Get the analytical water depth | ||
| 202 | const std::vector<Scalar>& getExactWaterDepth() const | ||
| 203 |
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1 | { return exactWaterDepth_; } |
| 204 | |||
| 205 | //! Get the analytical U-velocity | ||
| 206 | const std::vector<Scalar>& getExactVelocityX() const | ||
| 207 |
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1 | { return exactVelocityX_; } |
| 208 | |||
| 209 | //! Get the analytical V-velocity | ||
| 210 | const std::vector<Scalar>& getExactVelocityY() const | ||
| 211 |
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1 | { return exactVelocityY_; } |
| 212 | |||
| 213 | private: | ||
| 214 | ✗ | PrimaryVariables exactSol_(const GlobalPosition& globalPos) const | |
| 215 | { | ||
| 216 | 80 | PrimaryVariables values(0.0); | |
| 217 | 160 | const auto gravity = this->spatialParams().gravity(globalPos); | |
| 218 | 80 | const auto hSquared = waterDepthBoundary_*waterDepthBoundary_; | |
| 219 | 80 | const auto pressureGradient = 1000.0*gravity*bedSlope_; | |
| 220 | 160 | values[0] = waterDepthBoundary_; | |
| 221 | 160 | values[1] = pressureGradient*hSquared/(3.0*dynamicViscosity_); | |
| 222 | 160 | values[2] = 0.0; | |
| 223 | ✗ | return values; | |
| 224 | } | ||
| 225 | |||
| 226 | std::vector<Scalar> exactWaterDepth_; | ||
| 227 | std::vector<Scalar> exactVelocityX_; | ||
| 228 | std::vector<Scalar> exactVelocityY_; | ||
| 229 | |||
| 230 | Scalar channelWidth_; | ||
| 231 | Scalar waterDepthBoundary_; // water level | ||
| 232 | Scalar bedSlope_; // bed slope (positive downwards) | ||
| 233 | Scalar dynamicViscosity_; | ||
| 234 | |||
| 235 | static constexpr Scalar eps_ = 1.0e-6; | ||
| 236 | std::string name_; | ||
| 237 | }; | ||
| 238 | |||
| 239 | } //end namespace Dumux | ||
| 240 | |||
| 241 | #endif | ||
| 242 |