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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 NavierStokesTests | ||
| 10 | * \brief Test for the staggered grid Navier-Stokes model with analytical solution (Kovasznay 1948, \cite Kovasznay1948) | ||
| 11 | */ | ||
| 12 | |||
| 13 | #ifndef DUMUX_KOVASZNAY_TEST_PROBLEM_HH | ||
| 14 | #define DUMUX_KOVASZNAY_TEST_PROBLEM_HH | ||
| 15 | |||
| 16 | #include <dumux/common/properties.hh> | ||
| 17 | #include <dumux/common/parameters.hh> | ||
| 18 | #include <dumux/common/numeqvector.hh> | ||
| 19 | |||
| 20 | #include <dumux/freeflow/navierstokes/boundarytypes.hh> | ||
| 21 | #include <dumux/freeflow/navierstokes/staggered/problem.hh> | ||
| 22 | |||
| 23 | namespace Dumux { | ||
| 24 | |||
| 25 | /*! | ||
| 26 | * \ingroup NavierStokesTests | ||
| 27 | * \brief Test problem for the staggered grid (Kovasznay 1948, \cite Kovasznay1948) | ||
| 28 | * | ||
| 29 | * A two-dimensional Navier-Stokes flow with a periodicity in one direction | ||
| 30 | * is considered. The set-up represents a wake behind a two-dimensional grid | ||
| 31 | * and is chosen in a way such that an exact solution is available. | ||
| 32 | */ | ||
| 33 | template <class TypeTag> | ||
| 34 | 3 | class KovasznayTestProblem : public NavierStokesStaggeredProblem<TypeTag> | |
| 35 | { | ||
| 36 | using ParentType = NavierStokesStaggeredProblem<TypeTag>; | ||
| 37 | |||
| 38 | using BoundaryTypes = Dumux::NavierStokesBoundaryTypes<GetPropType<TypeTag, Properties::ModelTraits>::numEq()>; | ||
| 39 | using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>; | ||
| 40 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 41 | using SubControlVolume = typename GridGeometry::SubControlVolume; | ||
| 42 | using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>; | ||
| 43 | using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>; | ||
| 44 | using NumEqVector = Dumux::NumEqVector<PrimaryVariables>; | ||
| 45 | using Scalar = GetPropType<TypeTag, Properties::Scalar>; | ||
| 46 | using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>; | ||
| 47 | |||
| 48 | using Element = typename GridGeometry::GridView::template Codim<0>::Entity; | ||
| 49 | using GlobalPosition = typename Element::Geometry::GlobalCoordinate; | ||
| 50 | |||
| 51 | static constexpr auto upwindSchemeOrder = getPropValue<TypeTag, Properties::UpwindSchemeOrder>(); | ||
| 52 | |||
| 53 | public: | ||
| 54 | using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices; | ||
| 55 | |||
| 56 | 3 | KovasznayTestProblem(std::shared_ptr<const GridGeometry> gridGeometry) | |
| 57 |
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9 | : ParentType(gridGeometry) |
| 58 | { | ||
| 59 |
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6 | std::cout<< "upwindSchemeOrder is: " << GridGeometry::upwindStencilOrder() << "\n"; |
| 60 |
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3 | rho_ = getParam<Scalar>("Component.LiquidDensity", 1.0); |
| 61 |
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3 | kinematicViscosity_ = getParam<Scalar>("Component.LiquidKinematicViscosity", 1.0); |
| 62 | 3 | Scalar reynoldsNumber = 1.0 / kinematicViscosity_; | |
| 63 | 6 | lambda_ = 0.5 * reynoldsNumber | |
| 64 | 3 | - std::sqrt(reynoldsNumber * reynoldsNumber * 0.25 + 4.0 * M_PI * M_PI); | |
| 65 | 3 | } | |
| 66 | |||
| 67 | /*! | ||
| 68 | * \name Boundary conditions | ||
| 69 | */ | ||
| 70 | // \{ | ||
| 71 | |||
| 72 | /*! | ||
| 73 | * \brief Specifies which kind of boundary condition should be | ||
| 74 | * used for which equation on a given boundary control volume. | ||
| 75 | * | ||
| 76 | * \param globalPos The position of the center of the finite volume | ||
| 77 | */ | ||
| 78 | ✗ | BoundaryTypes boundaryTypesAtPos(const GlobalPosition &globalPos) const | |
| 79 | { | ||
| 80 | ✗ | BoundaryTypes values; | |
| 81 | |||
| 82 | // set Dirichlet values for the velocity everywhere | ||
| 83 | ✗ | values.setDirichlet(Indices::velocityXIdx); | |
| 84 | ✗ | values.setDirichlet(Indices::velocityYIdx); | |
| 85 | |||
| 86 | ✗ | return values; | |
| 87 | } | ||
| 88 | |||
| 89 | /*! | ||
| 90 | * \brief Returns whether a fixed Dirichlet value shall be used at a given cell. | ||
| 91 | * | ||
| 92 | * \param element The finite element | ||
| 93 | * \param fvGeometry The finite-volume geometry | ||
| 94 | * \param scv The sub control volume | ||
| 95 | * \param pvIdx The primary variable index in the solution vector | ||
| 96 | */ | ||
| 97 | ✗ | bool isDirichletCell(const Element& element, | |
| 98 | const FVElementGeometry& fvGeometry, | ||
| 99 | const SubControlVolume& scv, | ||
| 100 | int pvIdx) const | ||
| 101 | { | ||
| 102 | // set fixed pressure in all cells at the left boundary | ||
| 103 | 1054130 | auto isAtLeftBoundary = [&](const FVElementGeometry& fvGeometry) | |
| 104 | { | ||
| 105 |
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1015000 | if (fvGeometry.hasBoundaryScvf()) |
| 106 | { | ||
| 107 |
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183330 | for (const auto& scvf : scvfs(fvGeometry)) |
| 108 |
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118900 | if (scvf.boundary() && scvf.center()[0] < this->gridGeometry().bBoxMin()[0] + eps_) |
| 109 | 9960 | return true; | |
| 110 | } | ||
| 111 | return false; | ||
| 112 | }; | ||
| 113 |
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507500 | return (isAtLeftBoundary(fvGeometry) && pvIdx == Indices::pressureIdx); |
| 114 | } | ||
| 115 | |||
| 116 | /*! | ||
| 117 | * \brief Returns Dirichlet boundary values at a given position. | ||
| 118 | * | ||
| 119 | * \param globalPos The global position | ||
| 120 | */ | ||
| 121 | PrimaryVariables dirichletAtPos(const GlobalPosition & globalPos) const | ||
| 122 | { | ||
| 123 | // use the values of the analytical solution | ||
| 124 | 332375 | return analyticalSolution(globalPos); | |
| 125 | } | ||
| 126 | |||
| 127 | /*! | ||
| 128 | * \brief Returns the analytical solution of the problem at a given position. | ||
| 129 | * | ||
| 130 | * \param globalPos The global position | ||
| 131 | * \param time A parameter for consistent signatures. It is ignored here as this is a stationary test | ||
| 132 | */ | ||
| 133 | 381375 | PrimaryVariables analyticalSolution(const GlobalPosition& globalPos, Scalar time = 0.0) const | |
| 134 | { | ||
| 135 | 762750 | Scalar x = globalPos[0]; | |
| 136 | 762750 | Scalar y = globalPos[1]; | |
| 137 | |||
| 138 | PrimaryVariables values; | ||
| 139 | 762750 | values[Indices::pressureIdx] = rho_ * 0.5 * (1.0 - std::exp(2.0 * lambda_ * x)); | |
| 140 | 762750 | values[Indices::velocityXIdx] = 1.0 - std::exp(lambda_ * x) * std::cos(2.0 * M_PI * y); | |
| 141 | 762750 | values[Indices::velocityYIdx] = 0.5 * lambda_ / M_PI * std::exp(lambda_ * x) * std::sin(2.0 * M_PI * y); | |
| 142 | |||
| 143 | 381375 | return values; | |
| 144 | } | ||
| 145 | |||
| 146 | // \} | ||
| 147 | |||
| 148 | /*! | ||
| 149 | * \name Volume terms | ||
| 150 | */ | ||
| 151 | // \{ | ||
| 152 | |||
| 153 | /*! | ||
| 154 | * \brief Evaluates the initial value for a control volume. | ||
| 155 | * | ||
| 156 | * \param globalPos The global position | ||
| 157 | */ | ||
| 158 | ✗ | PrimaryVariables initialAtPos(const GlobalPosition &globalPos) const | |
| 159 | { | ||
| 160 | 2648492 | PrimaryVariables values; | |
| 161 | 2648492 | values[Indices::pressureIdx] = 0.0; | |
| 162 | 2648492 | values[Indices::velocityXIdx] = 0.0; | |
| 163 | 5296984 | values[Indices::velocityYIdx] = 0.0; | |
| 164 | |||
| 165 | ✗ | return values; | |
| 166 | } | ||
| 167 | |||
| 168 | private: | ||
| 169 | static constexpr Scalar eps_=1e-6; | ||
| 170 | |||
| 171 | Scalar rho_; | ||
| 172 | Scalar kinematicViscosity_; | ||
| 173 | Scalar lambda_; | ||
| 174 | }; | ||
| 175 | } // end namespace Dumux | ||
| 176 | |||
| 177 | #endif | ||
| 178 |