| Line | Branch | Exec | Source |
|---|---|---|---|
| 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 (bowl). | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_BOWL_TEST_PROBLEM_HH | ||
| 13 | #define DUMUX_BOWL_TEST_PROBLEM_HH | ||
| 14 | |||
| 15 | #include <dumux/common/boundarytypes.hh> | ||
| 16 | #include <dumux/common/properties.hh> | ||
| 17 | #include <dumux/common/parameters.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 wetting and drying test with sloshing water in a bowl. | ||
| 28 | * | ||
| 29 | * There is no flow over the boundaries and no friction is considered. | ||
| 30 | * | ||
| 31 | * This example is demanding for the implicit model if a high mesh resolution is applied | ||
| 32 | * (e.g. 150x150 cells) in combination with a large time step size. Using the new limiting | ||
| 33 | * (UpwindFluxLimiting = true) will help to improve the convergence for such cases. | ||
| 34 | * | ||
| 35 | * This test uses a low mesh resolution and only ensures that UpwindFluxLimiting for the mobility | ||
| 36 | * works. For low mesh resolution the solution is very diffusive so that the oscillation is dampened. | ||
| 37 | * This gets better with grid refinement (not tested here). | ||
| 38 | * | ||
| 39 | * The results are checked against a analytical solution which is based on the "Thacker-Solution" | ||
| 40 | * (William Thacker, "Some exact solutions to the nonlinear shallow-water wave equations", Journal | ||
| 41 | * of Fluid Mechanics, 107:499–508, 1981, doi: https://doi.org/10.1017/S0022112081001882). | ||
| 42 | * This implements the oscillating solution in a circular bowl (Section 4 in the paper). | ||
| 43 | * Further examples and details on the solution are given | ||
| 44 | * in SWASHES (Shallow Water Analytic Solutions for Hydraulic and Environmental Studies, | ||
| 45 | * https://www.idpoisson.fr/swashes/). | ||
| 46 | * | ||
| 47 | * This problem uses the \ref ShallowWaterModel. | ||
| 48 | */ | ||
| 49 | template <class TypeTag> | ||
| 50 | class BowlProblem : public ShallowWaterProblem<TypeTag> | ||
| 51 | { | ||
| 52 | using ParentType = ShallowWaterProblem<TypeTag>; | ||
| 53 | |||
| 54 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 55 | using FVElementGeometry = typename GetPropType<TypeTag, Properties::GridGeometry>::LocalView; | ||
| 56 | using SubControlVolume = typename FVElementGeometry::SubControlVolume; | ||
| 57 | using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace; | ||
| 58 | using GridView = typename GetPropType<TypeTag, Properties::GridGeometry>::GridView; | ||
| 59 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 60 | using GlobalPosition = typename Element::Geometry::GlobalCoordinate; | ||
| 61 | |||
| 62 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 63 | using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; | ||
| 64 | using NumEqVector = Dumux::NumEqVector<PrimaryVariables>; | ||
| 65 | |||
| 66 | using NeumannFluxes = NumEqVector; | ||
| 67 | using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView; | ||
| 68 | using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices; | ||
| 69 | using BoundaryTypes = Dumux::BoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>; | ||
| 70 | |||
| 71 | |||
| 72 | public: | ||
| 73 | 3 | BowlProblem(std::shared_ptr<const GridGeometry> gridGeometry) | |
| 74 |
7/20✓ Branch 1 taken 3 times.
✗ Branch 2 not taken.
✓ Branch 4 taken 3 times.
✗ Branch 5 not taken.
✓ Branch 8 taken 3 times.
✗ Branch 9 not taken.
✓ Branch 10 taken 3 times.
✗ Branch 11 not taken.
✗ Branch 12 not taken.
✓ Branch 13 taken 3 times.
✓ Branch 15 taken 3 times.
✗ Branch 16 not taken.
✓ Branch 18 taken 3 times.
✗ Branch 19 not taken.
✗ Branch 20 not taken.
✗ Branch 21 not taken.
✗ Branch 22 not taken.
✗ Branch 23 not taken.
✗ Branch 26 not taken.
✗ Branch 27 not taken.
|
9 | : ParentType(gridGeometry) |
| 75 | { | ||
| 76 | |||
| 77 |
2/4✓ Branch 1 taken 3 times.
✗ Branch 2 not taken.
✗ Branch 4 not taken.
✓ Branch 5 taken 3 times.
|
3 | name_ = getParam<std::string>("Problem.Name"); |
| 78 |
1/2✓ Branch 1 taken 3 times.
✗ Branch 2 not taken.
|
3 | bowlDepthAtCenter_ = getParam<Scalar>("Problem.BowlDepthAtCenter"); |
| 79 |
1/2✓ Branch 1 taken 3 times.
✗ Branch 2 not taken.
|
3 | bowlParaboloidRadius_ = getParam<Scalar>("Problem.BowlParaboloidRadius"); |
| 80 | |||
| 81 | // Thacker (1981) Eq. (43) | ||
| 82 | using std::sqrt; | ||
| 83 |
1/2✓ Branch 1 taken 3 times.
✗ Branch 2 not taken.
|
3 | bowlAnalyticParameterOmega_ = sqrt(8.0 * getParam<Scalar>("Problem.Gravity") * bowlDepthAtCenter_) / bowlParaboloidRadius_; |
| 84 | 3 | std::cout << "One full oscillation period of the water table is: " | |
| 85 |
1/2✓ Branch 2 taken 3 times.
✗ Branch 3 not taken.
|
6 | << oscillationPeriodInSeconds() << " seconds." << std::endl; |
| 86 | |||
| 87 | // Thacker (1981) Eq. (50) | ||
| 88 |
1/2✓ Branch 1 taken 3 times.
✗ Branch 2 not taken.
|
3 | const auto D0PlusEta = bowlDepthAtCenter_ + getParam<Scalar>("Problem.BowlInitialWaterElevationAtCenter"); |
| 89 | 3 | const auto D0PlusEtaSquared = D0PlusEta*D0PlusEta; | |
| 90 | 3 | const auto D0Squared = bowlDepthAtCenter_*bowlDepthAtCenter_; | |
| 91 | 3 | bowlAnalyticParameterA_ = (D0PlusEtaSquared - D0Squared)/(D0PlusEtaSquared + D0Squared); | |
| 92 | |||
| 93 | // check constraint Thacker (1981) text after Eq. (49) | ||
| 94 |
1/2✗ Branch 0 not taken.
✓ Branch 1 taken 3 times.
|
3 | if (bowlAnalyticParameterA_ >= 1.0) |
| 95 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Parameter A has to be smaller than unity!"); | |
| 96 | 3 | } | |
| 97 | |||
| 98 | //! One oscillation period of the water table (analytically this goes on forever) | ||
| 99 | ✗ | Scalar oscillationPeriodInSeconds() const | |
| 100 |
2/4✓ Branch 1 taken 3 times.
✗ Branch 2 not taken.
✓ Branch 4 taken 3 times.
✗ Branch 5 not taken.
|
6 | { return 2*M_PI/bowlAnalyticParameterOmega_; } |
| 101 | |||
| 102 | //! Get the analytical water depth at time t and position pos | ||
| 103 | 439520 | PrimaryVariables analyticalSolution(const Scalar t, const GlobalPosition& pos) const | |
| 104 | { | ||
| 105 | using std::sqrt; | ||
| 106 | using std::cos; | ||
| 107 | using std::sin; | ||
| 108 | |||
| 109 | // see Thacker (1981) Eq. (51) for formula | ||
| 110 |
8/8✓ Branch 0 taken 213440 times.
✓ Branch 1 taken 226080 times.
✓ Branch 2 taken 213440 times.
✓ Branch 3 taken 226080 times.
✓ Branch 4 taken 213440 times.
✓ Branch 5 taken 226080 times.
✓ Branch 6 taken 213440 times.
✓ Branch 7 taken 226080 times.
|
1758080 | const auto radiusSquared = pos[0]*pos[0] + pos[1]*pos[1]; |
| 111 | 439520 | const auto LSquared = bowlParaboloidRadius_*bowlParaboloidRadius_; | |
| 112 | 439520 | const auto A = bowlAnalyticParameterA_; | |
| 113 | 439520 | const auto omega = bowlAnalyticParameterOmega_; | |
| 114 | 439520 | const auto D0 = bowlDepthAtCenter_; | |
| 115 | |||
| 116 | 439520 | const auto oneMinusASq = 1.0 - A*A; | |
| 117 | 439520 | const auto oneMinusACosOmegaT = 1.0 - A*cos(omega*t); | |
| 118 | 439520 | const auto ratioSq = oneMinusASq / (oneMinusACosOmegaT*oneMinusACosOmegaT); | |
| 119 | 439520 | const auto localRadiusSq = radiusSquared / LSquared; | |
| 120 | // bowl depth function (cf. D in Thacker (1981)) | ||
| 121 | 439520 | const auto D = D0*(1.0 - localRadiusSq); | |
| 122 | // height above equilibrium water level (cf. h in Thacker (1981)) | ||
| 123 | 439520 | const auto h = D0*(sqrt(ratioSq) - 1.0 - localRadiusSq*(ratioSq - 1.0)); | |
| 124 | // see remark about total water depth in Thacker (1981) beginning section 2 | ||
| 125 | 439520 | const auto analyticalWaterDepth = h + D; | |
| 126 | |||
| 127 | 439520 | const auto halfOmegaASinOmegaT = 0.5*omega*A*sin(omega*t); | |
| 128 |
2/2✓ Branch 0 taken 213440 times.
✓ Branch 1 taken 226080 times.
|
439520 | const auto analyticalVelocityX = pos[0]*halfOmegaASinOmegaT/oneMinusACosOmegaT; |
| 129 |
2/2✓ Branch 0 taken 213440 times.
✓ Branch 1 taken 226080 times.
|
439520 | const auto analyticalVelocityY = pos[1]*halfOmegaASinOmegaT/oneMinusACosOmegaT; |
| 130 | |||
| 131 | // The radius of the shoreline (where h + D = 0), Eq. (48) | ||
| 132 | 439520 | const auto h0 = D0*(sqrt(ratioSq) - 1.0); // h in the middle of the bowl (r=0) | |
| 133 | 439520 | const auto shoreLineRadiusSquared = LSquared*(D0/(D0 + h0)); | |
| 134 | |||
| 135 | // outside shoreline the water height and velocity is zero | ||
| 136 |
2/2✓ Branch 0 taken 213440 times.
✓ Branch 1 taken 226080 times.
|
439520 | if (radiusSquared > shoreLineRadiusSquared) |
| 137 | 213440 | return { 0.0, 0.0, 0.0 }; | |
| 138 | else | ||
| 139 | 226080 | return { analyticalWaterDepth, analyticalVelocityX, analyticalVelocityY }; | |
| 140 | } | ||
| 141 | |||
| 142 | /*! | ||
| 143 | * \name Problem parameters | ||
| 144 | */ | ||
| 145 | // \{ | ||
| 146 | |||
| 147 | /*! | ||
| 148 | * \brief The problem name | ||
| 149 | * This is used as a prefix for files generated by the simulation. | ||
| 150 | */ | ||
| 151 | const std::string& name() const | ||
| 152 |
1/2✓ Branch 1 taken 3 times.
✗ Branch 2 not taken.
|
3 | { return name_; } |
| 153 | |||
| 154 | // \} | ||
| 155 | |||
| 156 | /*! | ||
| 157 | * \name Boundary conditions | ||
| 158 | */ | ||
| 159 | // \{ | ||
| 160 | |||
| 161 | /*! | ||
| 162 | * \brief Specifies which kind of boundary condition should be | ||
| 163 | * used for which equation on a given boundary segment. | ||
| 164 | */ | ||
| 165 | ✗ | BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const | |
| 166 | { | ||
| 167 | 868320 | BoundaryTypes bcTypes; | |
| 168 |
2/4✗ Branch 0 not taken.
✓ Branch 1 taken 173664 times.
✗ Branch 2 not taken.
✓ Branch 3 taken 694656 times.
|
868320 | bcTypes.setAllNeumann(); |
| 169 | ✗ | return bcTypes; | |
| 170 | } | ||
| 171 | |||
| 172 | /*! | ||
| 173 | * \brief Specifies the neumann boundary | ||
| 174 | * | ||
| 175 | * We need the Riemann invariants to compute the values depending of the boundary type. | ||
| 176 | * Since we use a weak imposition we do not have a dirichlet value. We impose fluxes | ||
| 177 | * based on q, h, etc. computed with the Riemann invariants | ||
| 178 | */ | ||
| 179 | template<class ElementFluxVariablesCache> | ||
| 180 | 694656 | NeumannFluxes neumann(const Element& element, | |
| 181 | const FVElementGeometry& fvGeometry, | ||
| 182 | const ElementVolumeVariables& elemVolVars, | ||
| 183 | const ElementFluxVariablesCache& elemFluxVarsCache, | ||
| 184 | const SubControlVolumeFace& scvf) const | ||
| 185 | { | ||
| 186 | 694656 | NeumannFluxes values(0.0); | |
| 187 | |||
| 188 | 1389312 | const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx()); | |
| 189 | 694656 | const auto& insideVolVars = elemVolVars[insideScv]; | |
| 190 | 694656 | const auto& nxy = scvf.unitOuterNormal(); | |
| 191 | 1389312 | const auto gravity = this->spatialParams().gravity(scvf.center()); | |
| 192 | std::array<Scalar, 3> boundaryStateVariables; | ||
| 193 | |||
| 194 | //no flow with zero normal velocity and tangential velocity | ||
| 195 | 2778624 | const auto vNormalGhost = -(nxy[0] * insideVolVars.velocity(0) + nxy[1] * insideVolVars.velocity(1)); | |
| 196 | 2778624 | const auto vTangentialGhost = -nxy[1] * insideVolVars.velocity(0) + nxy[0] * insideVolVars.velocity(1); | |
| 197 | |||
| 198 | 1389312 | boundaryStateVariables[0] = insideVolVars.waterDepth(); | |
| 199 | 2083968 | boundaryStateVariables[1] = nxy[0] * vNormalGhost - nxy[1] * vTangentialGhost; | |
| 200 | 2083968 | boundaryStateVariables[2] = nxy[1] * vNormalGhost + nxy[0] * vTangentialGhost; | |
| 201 | |||
| 202 | const auto riemannFlux = | ||
| 203 | 2083968 | ShallowWater::riemannProblem(insideVolVars.waterDepth(), boundaryStateVariables[0], | |
| 204 | 1389312 | insideVolVars.velocity(0), boundaryStateVariables[1], | |
| 205 | 1389312 | insideVolVars.velocity(1), boundaryStateVariables[2], | |
| 206 | insideVolVars.bedSurface(), insideVolVars.bedSurface(), | ||
| 207 | gravity, nxy); | ||
| 208 | |||
| 209 | 2083968 | values[Indices::massBalanceIdx] = riemannFlux[0]; | |
| 210 | 2083968 | values[Indices::velocityXIdx] = riemannFlux[1]; | |
| 211 | 2083968 | values[Indices::velocityYIdx] = riemannFlux[2]; | |
| 212 | |||
| 213 | 694656 | return values; | |
| 214 | } | ||
| 215 | |||
| 216 | // \} | ||
| 217 | |||
| 218 | /*! | ||
| 219 | * \name Volume terms | ||
| 220 | */ | ||
| 221 | // \{ | ||
| 222 | |||
| 223 | /*! | ||
| 224 | * \brief Evaluate the initial values at position globalPos | ||
| 225 | */ | ||
| 226 | 3280 | PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const | |
| 227 | { | ||
| 228 | using std::max; // regularize so that we are virtually dry but not completely dry | ||
| 229 |
4/4✓ Branch 1 taken 1844 times.
✓ Branch 2 taken 1436 times.
✓ Branch 3 taken 1844 times.
✓ Branch 4 taken 1436 times.
|
5124 | return { max(analyticalSolution(0, globalPos)[0], 1e-5), 0.0, 0.0 }; |
| 230 | }; | ||
| 231 | |||
| 232 | // \} | ||
| 233 | |||
| 234 | private: | ||
| 235 | Scalar bowlDepthAtCenter_; | ||
| 236 | Scalar bowlParaboloidRadius_; | ||
| 237 | Scalar bowlAnalyticParameterOmega_; | ||
| 238 | Scalar bowlAnalyticParameterA_; | ||
| 239 | static constexpr Scalar eps_ = 1.0e-6; | ||
| 240 | std::string name_; | ||
| 241 | }; | ||
| 242 | |||
| 243 | } //end namespace Dumux | ||
| 244 | |||
| 245 | #endif | ||
| 246 |