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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 | * \file | ||
| 9 | * \ingroup ShallowWaterTests | ||
| 10 | * \brief A test for the Shallow water model (rough channel). | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_ROUGH_CHANNEL_TEST_PROBLEM_HH | ||
| 13 | #define DUMUX_ROUGH_CHANNEL_TEST_PROBLEM_HH | ||
| 14 | |||
| 15 | #include <dumux/common/boundarytypes.hh> | ||
| 16 | #include <dumux/common/parameters.hh> | ||
| 17 | #include <dumux/common/properties.hh> | ||
| 18 | #include <dumux/common/numeqvector.hh> | ||
| 19 | |||
| 20 | #include <dumux/freeflow/shallowwater/problem.hh> | ||
| 21 | #include <dumux/freeflow/shallowwater/boundaryfluxes.hh> | ||
| 22 | |||
| 23 | namespace Dumux { | ||
| 24 | |||
| 25 | /*! | ||
| 26 | * \ingroup ShallowWaterTests | ||
| 27 | * \brief A simple flow in a rough channel with friction law after Manning. | ||
| 28 | * | ||
| 29 | * At the left border a discharge | ||
| 30 | * boundary condition is applied and at the right border a water depth boundary condition. | ||
| 31 | * All other boundaries are set to no-flow. Normal flow is assumed, therefore the water depth | ||
| 32 | * at the right border can be calculated with the formular of Gaukler-Manning-Strickler. | ||
| 33 | * | ||
| 34 | * \f[ | ||
| 35 | * v_m = 1/n * R_{hy}^{2/3} * I_s^{1/2} | ||
| 36 | * \f] | ||
| 37 | * | ||
| 38 | * With the mean velocity | ||
| 39 | * \f[ | ||
| 40 | * v_m = \frac{q}/{h} | ||
| 41 | * \f] | ||
| 42 | * the friction value n after Manning | ||
| 43 | * the hydraulic radius R_{hy} equal to the water depth h (because normal flow is assumed) | ||
| 44 | * the bed slope I_s and the unity inflow discharge q. | ||
| 45 | * | ||
| 46 | * Therefore h can be calculated with | ||
| 47 | * | ||
| 48 | * \f[ | ||
| 49 | * h = \left(\frac{n*q}{\sqrt{I_s}} \right)^{3/5} | ||
| 50 | * \f] | ||
| 51 | * | ||
| 52 | * The formula of Gaukler Manning and Strickler is also used to calculate the analytic solution. | ||
| 53 | * | ||
| 54 | * This problem uses the \ref ShallowWaterModel | ||
| 55 | */ | ||
| 56 | template <class TypeTag> | ||
| 57 | class RoughChannelProblem : public ShallowWaterProblem<TypeTag> | ||
| 58 | { | ||
| 59 | using ParentType = ShallowWaterProblem<TypeTag>; | ||
| 60 | using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; | ||
| 61 | using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>; | ||
| 62 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 63 | using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices; | ||
| 64 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 65 | using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView; | ||
| 66 | using GridVariables = GetPropType<TypeTag, Properties::GridVariables>; | ||
| 67 | using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView; | ||
| 68 | using VolumeVariables = typename ElementVolumeVariables::VolumeVariables; | ||
| 69 | using FVElementGeometry = typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView; | ||
| 70 | using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace; | ||
| 71 | using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView; | ||
| 72 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 73 | using GlobalPosition = typename Element::Geometry::GlobalCoordinate; | ||
| 74 | using NumEqVector = Dumux::NumEqVector<PrimaryVariables>; | ||
| 75 | using NeumannFluxes = NumEqVector; | ||
| 76 | using SubControlVolume = typename FVElementGeometry::SubControlVolume; | ||
| 77 | |||
| 78 | public: | ||
| 79 | 1 | RoughChannelProblem(std::shared_ptr<const GridGeometry> gridGeometry) | |
| 80 |
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3 | : ParentType(gridGeometry) |
| 81 | { | ||
| 82 |
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1 | name_ = getParam<std::string>("Problem.Name"); |
| 83 |
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2 | exactWaterDepth_.resize(gridGeometry->numDofs(), 0.0); |
| 84 |
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2 | exactVelocityX_.resize(gridGeometry->numDofs(), 0.0); |
| 85 |
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1 | constManningN_ = getParam<Scalar>("Problem.ManningN"); |
| 86 |
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1 | bedSlope_ = getParam<Scalar>("Problem.BedSlope"); |
| 87 |
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1 | discharge_ = getParam<Scalar>("Problem.Discharge"); |
| 88 | 1 | hBoundary_ = this->gauklerManningStrickler(discharge_,constManningN_,bedSlope_); | |
| 89 | 1 | } | |
| 90 | |||
| 91 | //! Get the analytical water depth | ||
| 92 | const std::vector<Scalar>& getExactWaterDepth() | ||
| 93 | { | ||
| 94 |
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1 | return exactWaterDepth_; |
| 95 | } | ||
| 96 | |||
| 97 | //! Get the analytical velocity | ||
| 98 | const std::vector<Scalar>& getExactVelocityX() | ||
| 99 | { | ||
| 100 |
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1 | return exactVelocityX_; |
| 101 | } | ||
| 102 | |||
| 103 | //! Calculate the water depth with Gaukler-Manning-Strickler | ||
| 104 | ✗ | Scalar gauklerManningStrickler(Scalar discharge, Scalar manningN, Scalar bedSlope) | |
| 105 | { | ||
| 106 | using std::pow; | ||
| 107 | using std::abs; | ||
| 108 | using std::sqrt; | ||
| 109 | |||
| 110 | ✗ | return pow(abs(discharge)*manningN/sqrt(bedSlope), 0.6); | |
| 111 | } | ||
| 112 | |||
| 113 | //! Update the analytical solution | ||
| 114 | 24 | void updateAnalyticalSolution() | |
| 115 | { | ||
| 116 | using std::abs; | ||
| 117 | |||
| 118 |
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120072 | for (const auto& element : elements(this->gridGeometry().gridView())) |
| 119 | { | ||
| 120 | 60000 | const Scalar h = this->gauklerManningStrickler(discharge_,constManningN_,bedSlope_); | |
| 121 | 60000 | const Scalar u = abs(discharge_)/h; | |
| 122 | |||
| 123 | 180000 | const auto eIdx = this->gridGeometry().elementMapper().index(element); | |
| 124 | 120000 | exactWaterDepth_[eIdx] = h; | |
| 125 | 120000 | exactVelocityX_[eIdx] = u; | |
| 126 | } | ||
| 127 | 24 | } | |
| 128 | |||
| 129 | /*! | ||
| 130 | * \name Problem parameters | ||
| 131 | */ | ||
| 132 | // \{ | ||
| 133 | |||
| 134 | /*! | ||
| 135 | * \brief The problem name | ||
| 136 | * | ||
| 137 | * This is used as a prefix for files generated by the simulation. | ||
| 138 | */ | ||
| 139 | const std::string& name() const | ||
| 140 | { | ||
| 141 |
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1 | return name_; |
| 142 | } | ||
| 143 | |||
| 144 | /*! | ||
| 145 | * \brief Evaluate the source term for all balance equations within a given | ||
| 146 | * sub-control-volume. | ||
| 147 | * | ||
| 148 | * This is the method for the case where the source term is | ||
| 149 | * potentially solution dependent and requires some quantities that | ||
| 150 | * are specific to the fully-implicit method. | ||
| 151 | * | ||
| 152 | * \param element The finite element | ||
| 153 | * \param fvGeometry The finite-volume geometry | ||
| 154 | * \param elemVolVars All volume variables for the element | ||
| 155 | * \param scv The sub control volume | ||
| 156 | * | ||
| 157 | * For this method, the \a values parameter stores the conserved quantity rate | ||
| 158 | * generated or annihilate per volume unit. Positive values mean | ||
| 159 | * that the conserved quantity is created, negative ones mean that it vanishes. | ||
| 160 | * E.g. for the mass balance that would be a mass rate in \f$ [ kg / (m^3 \cdot s)] \f$. | ||
| 161 | */ | ||
| 162 | 523835 | NumEqVector source(const Element& element, | |
| 163 | const FVElementGeometry& fvGeometry, | ||
| 164 | const ElementVolumeVariables& elemVolVars, | ||
| 165 | const SubControlVolume &scv) const | ||
| 166 | { | ||
| 167 | |||
| 168 | 523835 | NumEqVector source (0.0); | |
| 169 | |||
| 170 | 523835 | source += bottomFrictionSource(element, fvGeometry, elemVolVars, scv); | |
| 171 | |||
| 172 | 523835 | return source; | |
| 173 | } | ||
| 174 | |||
| 175 | /*! | ||
| 176 | * \brief Compute the source term due to bottom friction | ||
| 177 | * | ||
| 178 | * \param element The finite element | ||
| 179 | * \param fvGeometry The finite-volume geometry | ||
| 180 | * \param elemVolVars All volume variables for the element | ||
| 181 | * \param scv The sub control volume | ||
| 182 | * | ||
| 183 | * \return source | ||
| 184 | */ | ||
| 185 | 523835 | NumEqVector bottomFrictionSource(const Element& element, | |
| 186 | const FVElementGeometry& fvGeometry, | ||
| 187 | const ElementVolumeVariables& elemVolVars, | ||
| 188 | const SubControlVolume &scv) const | ||
| 189 | { | ||
| 190 | 523835 | NumEqVector bottomFrictionSource(0.0); | |
| 191 | |||
| 192 | 523835 | const auto& volVars = elemVolVars[scv]; | |
| 193 | 1571505 | Dune::FieldVector<Scalar, 2> bottomShearStress = this->spatialParams().frictionLaw(element, scv).bottomShearStress(volVars); | |
| 194 | |||
| 195 | 1047670 | bottomFrictionSource[0] = 0.0; | |
| 196 | 2095340 | bottomFrictionSource[1] = -bottomShearStress[0] / volVars.density(); | |
| 197 | 2095340 | bottomFrictionSource[2] = -bottomShearStress[1] / volVars.density(); | |
| 198 | |||
| 199 | 523835 | return bottomFrictionSource; | |
| 200 | } | ||
| 201 | |||
| 202 | // \} | ||
| 203 | |||
| 204 | /*! | ||
| 205 | * \name Boundary conditions | ||
| 206 | */ | ||
| 207 | // \{ | ||
| 208 | |||
| 209 | /*! | ||
| 210 | * \brief Specifies which kind of boundary condition should be | ||
| 211 | * used for which equation on a given boundary segment. | ||
| 212 | * | ||
| 213 | * \param globalPos The position for which the boundary type is set | ||
| 214 | */ | ||
| 215 | ✗ | BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const | |
| 216 | { | ||
| 217 | 268256 | BoundaryTypes bcTypes; | |
| 218 |
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268256 | bcTypes.setAllNeumann(); |
| 219 | ✗ | return bcTypes; | |
| 220 | } | ||
| 221 | |||
| 222 | /*! | ||
| 223 | * \brief Specifies the neumann boundary | ||
| 224 | * | ||
| 225 | * We need the Riemann invariants to compute the values depending of the boundary type. | ||
| 226 | * Since we use a weak imposition we do not have a dirichlet value. We impose fluxes | ||
| 227 | * based on q, h, etc. computed with the Riemann invariants | ||
| 228 | * | ||
| 229 | * \param element | ||
| 230 | * \param fvGeometry | ||
| 231 | * \param elemVolVars | ||
| 232 | * \param elemFluxVarsCache | ||
| 233 | * \param scvf | ||
| 234 | */ | ||
| 235 | 211696 | NeumannFluxes neumann(const Element& element, | |
| 236 | const FVElementGeometry& fvGeometry, | ||
| 237 | const ElementVolumeVariables& elemVolVars, | ||
| 238 | const ElementFluxVariablesCache& elemFluxVarsCache, | ||
| 239 | const SubControlVolumeFace& scvf) const | ||
| 240 | { | ||
| 241 | 211696 | NeumannFluxes values(0.0); | |
| 242 | |||
| 243 | 423392 | const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx()); | |
| 244 | 211696 | const auto& insideVolVars = elemVolVars[insideScv]; | |
| 245 |
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211696 | const auto& nxy = scvf.unitOuterNormal(); |
| 246 |
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423392 | const auto gravity = this->spatialParams().gravity(scvf.center()); |
| 247 | std::array<Scalar, 3> boundaryStateVariables; | ||
| 248 | |||
| 249 | // impose discharge at the left side | ||
| 250 |
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1270176 | if (scvf.center()[0] < this->gridGeometry().bBoxMin()[0] + eps_) |
| 251 | { | ||
| 252 | 4180 | boundaryStateVariables = ShallowWater::fixedDischargeBoundary(discharge_, | |
| 253 | insideVolVars.waterDepth(), | ||
| 254 | insideVolVars.velocity(0), | ||
| 255 | insideVolVars.velocity(1), | ||
| 256 | gravity, | ||
| 257 | nxy); | ||
| 258 | } | ||
| 259 | // impose water depth at the right side | ||
| 260 |
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1263906 | else if (scvf.center()[0] > this->gridGeometry().bBoxMax()[0] - eps_) |
| 261 | { | ||
| 262 | 4480 | boundaryStateVariables = ShallowWater::fixedWaterDepthBoundary(hBoundary_, | |
| 263 | insideVolVars.waterDepth(), | ||
| 264 | insideVolVars.velocity(0), | ||
| 265 | insideVolVars.velocity(1), | ||
| 266 | gravity, | ||
| 267 | nxy); | ||
| 268 | } | ||
| 269 | // no flow boundary | ||
| 270 | else | ||
| 271 | { | ||
| 272 | 419062 | boundaryStateVariables[0] = insideVolVars.waterDepth(); | |
| 273 | 419062 | boundaryStateVariables[1] = -insideVolVars.velocity(0); | |
| 274 | 628593 | boundaryStateVariables[2] = -insideVolVars.velocity(1); | |
| 275 | } | ||
| 276 | |||
| 277 | 211696 | auto riemannFlux = ShallowWater::riemannProblem(insideVolVars.waterDepth(), | |
| 278 | 423392 | boundaryStateVariables[0], | |
| 279 | insideVolVars.velocity(0), | ||
| 280 | 423392 | boundaryStateVariables[1], | |
| 281 | insideVolVars.velocity(1), | ||
| 282 | 423392 | boundaryStateVariables[2], | |
| 283 | insideVolVars.bedSurface(), | ||
| 284 | insideVolVars.bedSurface(), | ||
| 285 | gravity, | ||
| 286 | nxy); | ||
| 287 | |||
| 288 | 635088 | values[Indices::massBalanceIdx] = riemannFlux[0]; | |
| 289 | 635088 | values[Indices::velocityXIdx] = riemannFlux[1]; | |
| 290 | 635088 | values[Indices::velocityYIdx] = riemannFlux[2]; | |
| 291 | |||
| 292 | 211696 | return values; | |
| 293 | } | ||
| 294 | |||
| 295 | // \} | ||
| 296 | |||
| 297 | /*! | ||
| 298 | * \name Volume terms | ||
| 299 | */ | ||
| 300 | // \{ | ||
| 301 | |||
| 302 | /*! | ||
| 303 | * \brief Evaluate the initial values for a control volume. | ||
| 304 | * | ||
| 305 | * For this method, the \a values parameter stores primary | ||
| 306 | * variables. | ||
| 307 | * | ||
| 308 | * \param globalPos The position for which the boundary type is set | ||
| 309 | */ | ||
| 310 | ✗ | PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const | |
| 311 | { | ||
| 312 | 2500 | PrimaryVariables values(0.0); | |
| 313 | |||
| 314 | 5000 | values[0] = hBoundary_; | |
| 315 | 7500 | values[1] = abs(discharge_)/hBoundary_; | |
| 316 | 5000 | values[2] = 0.0; | |
| 317 | |||
| 318 | ✗ | return values; | |
| 319 | }; | ||
| 320 | |||
| 321 | // \} | ||
| 322 | |||
| 323 | private: | ||
| 324 | std::vector<Scalar> exactWaterDepth_; | ||
| 325 | std::vector<Scalar> exactVelocityX_; | ||
| 326 | Scalar hBoundary_; | ||
| 327 | Scalar constManningN_; // analytic solution is only available for const friction. | ||
| 328 | Scalar bedSlope_; | ||
| 329 | Scalar discharge_; // discharge at the inflow boundary | ||
| 330 | static constexpr Scalar eps_ = 1.0e-6; | ||
| 331 | std::string name_; | ||
| 332 | }; | ||
| 333 | |||
| 334 | } //end namespace Dumux | ||
| 335 | |||
| 336 | #endif | ||
| 337 |