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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 Discretization | ||
| 10 | * \brief Helper classes to compute the integration elements | ||
| 11 | * | ||
| 12 | * Provides area, volume, and integration elements for integration formulas. | ||
| 13 | * Modifying these quantities is useful to realize extrusions of the computational domain. | ||
| 14 | */ | ||
| 15 | #ifndef DUMUX_DISCRETIZATION_EXTRUSION_HH | ||
| 16 | #define DUMUX_DISCRETIZATION_EXTRUSION_HH | ||
| 17 | |||
| 18 | #include <dune/common/std/type_traits.hh> | ||
| 19 | |||
| 20 | namespace Dumux { | ||
| 21 | |||
| 22 | /*! | ||
| 23 | * \ingroup Discretization | ||
| 24 | * \brief Default implementation that performs no extrusion (extrusion with identity) | ||
| 25 | */ | ||
| 26 | struct NoExtrusion | ||
| 27 | { | ||
| 28 | template<class FVGeo, class SCVF> | ||
| 29 | ✗ | static constexpr auto area(const FVGeo&, const SCVF& scvf) | |
| 30 |
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4962864824 | { return scvf.area(); } |
| 31 | |||
| 32 | template<class FVGeo, class SCV> | ||
| 33 | ✗ | static constexpr auto volume(const FVGeo&, const SCV& scv) | |
| 34 |
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1229779736 | { return scv.volume(); } |
| 35 | |||
| 36 | template<class Geometry> | ||
| 37 | static constexpr auto integrationElement(const Geometry& geo, const typename Geometry::LocalCoordinate& x) | ||
| 38 |
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778623 | { return geo.integrationElement(x); } |
| 39 | }; | ||
| 40 | |||
| 41 | /*! | ||
| 42 | * \ingroup Discretization | ||
| 43 | * \brief Rotation symmetric extrusion policy for rotating about an external axis | ||
| 44 | * \tparam radAx The radial axis perpendicular to the symmetry axis (0 = x, 1 = y) | ||
| 45 | */ | ||
| 46 | template<int radAx = 0> | ||
| 47 | struct RotationalExtrusion | ||
| 48 | { | ||
| 49 | static constexpr int radialAxis = radAx; | ||
| 50 | |||
| 51 | /*! | ||
| 52 | * \brief Transformed sub-control-volume face area | ||
| 53 | * \note Mid-point rule integrals are only exact for constants | ||
| 54 | */ | ||
| 55 | template<class FVGeo, class SCVF> | ||
| 56 | ✗ | static constexpr auto area(const FVGeo&, const SCVF& scvf) | |
| 57 | { | ||
| 58 | static_assert(int(SCVF::Traits::Geometry::mydimension) == int(SCVF::Traits::Geometry::coorddimension-1), "Area element to be called with a codim-1-entity!"); | ||
| 59 | static_assert(SCVF::Traits::Geometry::coorddimension <= 2, "Axis rotation only makes sense for geometries up to 2D!"); | ||
| 60 | static_assert(radialAxis < int(SCVF::Traits::Geometry::coorddimension), "Illegal radial axis!"); | ||
| 61 | |||
| 62 | // Guldinus theorem | ||
| 63 |
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124596874 | return scvf.area()*2.0*M_PI*scvf.center()[radialAxis]; |
| 64 | } | ||
| 65 | |||
| 66 | /*! | ||
| 67 | * \brief Transformed sub-control-volume volume | ||
| 68 | * \note Mid-point rule integrals are only exact for constants | ||
| 69 | */ | ||
| 70 | template<class FVGeo, class SCV> | ||
| 71 | ✗ | static constexpr auto volume(const FVGeo&, const SCV& scv) | |
| 72 | { | ||
| 73 | static_assert(int(SCV::Traits::Geometry::mydimension) == int(SCV::Traits::Geometry::coorddimension), "Volume element to be called with a codim-0-entity!"); | ||
| 74 | static_assert(SCV::Traits::Geometry::coorddimension <= 2, "Axis rotation only makes sense for geometries up to 2D!"); | ||
| 75 | static_assert(radialAxis < int(SCV::Traits::Geometry::coorddimension), "Illegal radial axis!"); | ||
| 76 | |||
| 77 | // Guldinus theorem | ||
| 78 |
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67996960 | return scv.volume()*2.0*M_PI*scv.center()[radialAxis]; |
| 79 | } | ||
| 80 | |||
| 81 | /*! | ||
| 82 | * \brief Integration element for quadrature rules on the reference element | ||
| 83 | */ | ||
| 84 | template<class Geometry> | ||
| 85 | 9600 | static constexpr auto integrationElement(const Geometry& geo, const typename Geometry::LocalCoordinate& x) | |
| 86 | { | ||
| 87 | static_assert(Geometry::coorddimension <= 2, "Axis rotation only makes sense for geometries up to 2D!"); | ||
| 88 | static_assert(radialAxis < int(Geometry::coorddimension), "Illegal radial axis!"); | ||
| 89 | |||
| 90 | // Multiply with the polar extrusion factor (2*pi) and the determinant of the transformation Jacobian (radius) | ||
| 91 | 19290 | return geo.integrationElement(x)*2.0*M_PI*geo.global(x)[radialAxis]; | |
| 92 | } | ||
| 93 | }; | ||
| 94 | |||
| 95 | /*! | ||
| 96 | * \ingroup Discretization | ||
| 97 | * \brief Rotation symmetric extrusion policy for spherical rotation | ||
| 98 | */ | ||
| 99 | struct SphericalExtrusion | ||
| 100 | { | ||
| 101 | /*! | ||
| 102 | * \brief Transformed sub-control-volume face area | ||
| 103 | * \note Mid-point rule integrals are only exact for constants | ||
| 104 | */ | ||
| 105 | template<class FVGeo, class SCVF> | ||
| 106 | ✗ | static constexpr auto area(const FVGeo&, const SCVF& scvf) | |
| 107 | { | ||
| 108 | static_assert(int(SCVF::Traits::Geometry::mydimension) == int(SCVF::Traits::Geometry::coorddimension-1), "Area element to be called with a codim-1-entity!"); | ||
| 109 | static_assert(SCVF::Traits::Geometry::coorddimension == 1, "Spherical rotation only makes sense for 1D geometries!"); | ||
| 110 | |||
| 111 | // sphere surface area | ||
| 112 |
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12 | const auto radius = scvf.center()[0]; |
| 113 |
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12 | return 4.0*M_PI*radius*radius; |
| 114 | } | ||
| 115 | |||
| 116 | /*! | ||
| 117 | * \brief Transformed sub-control-volume volume | ||
| 118 | * \note Mid-point rule integrals are only exact for constants | ||
| 119 | */ | ||
| 120 | template<class FVGeo, class SCV> | ||
| 121 | 20 | static constexpr auto volume(const FVGeo& fvGeometry, const SCV& scv) | |
| 122 | { | ||
| 123 | static_assert(int(SCV::Traits::Geometry::mydimension) == int(SCV::Traits::Geometry::coorddimension), "Volume element to be called with a codim-0-entity!"); | ||
| 124 | static_assert(SCV::Traits::Geometry::coorddimension == 1, "Spherical rotation only makes sense for 1D geometries!"); | ||
| 125 | |||
| 126 | // subtract two balls | ||
| 127 | 20 | const auto geo = fvGeometry.geometry(scv); | |
| 128 | 40 | const auto radius0 = geo.corner(0)[0]; | |
| 129 | 40 | const auto radius1 = geo.corner(1)[0]; | |
| 130 | using std::abs; | ||
| 131 | 40 | return 4.0/3.0*M_PI*abs(radius1*radius1*radius1 - radius0*radius0*radius0); | |
| 132 | } | ||
| 133 | |||
| 134 | /*! | ||
| 135 | * \brief Integration element for quadrature rules on the reference element | ||
| 136 | */ | ||
| 137 | template<class Geometry> | ||
| 138 | ✗ | static constexpr auto integrationElement(const Geometry& geo, const typename Geometry::LocalCoordinate& x) | |
| 139 | { | ||
| 140 | static_assert(Geometry::coorddimension == 1, "Spherical rotation only makes sense for 1D geometries!"); | ||
| 141 | |||
| 142 | // Multiply with the constant spherical extrusion factor (int_0^2pi int_0^pi sin(phi) dphi dtheta = 4pi) | ||
| 143 | // and the remaining (radius-dependent) part of determinant of the transformation Jacobian (radius*radius) | ||
| 144 | 30 | const auto radius = geo.global(x)[0]; | |
| 145 | 60 | return geo.integrationElement(x)*4.0*M_PI*radius*radius; | |
| 146 | } | ||
| 147 | }; | ||
| 148 | |||
| 149 | /*! | ||
| 150 | * \brief Traits extracting the public Extrusion type from T | ||
| 151 | * Defaults to NoExtrusion if no such type is found | ||
| 152 | */ | ||
| 153 | template<class T> | ||
| 154 | class Extrusion | ||
| 155 | { | ||
| 156 | template<class G> | ||
| 157 | using E = typename G::Extrusion; | ||
| 158 | public: | ||
| 159 | using type = typename Dune::Std::detected_or<NoExtrusion, E, T>::type; | ||
| 160 | }; | ||
| 161 | |||
| 162 | /*! | ||
| 163 | * \brief Convenience alias for obtaining the extrusion type | ||
| 164 | */ | ||
| 165 | template<class T> | ||
| 166 | using Extrusion_t = typename Extrusion<T>::type; | ||
| 167 | |||
| 168 | /*! | ||
| 169 | * \brief Convenience trait to check whether the extrusion is rotational | ||
| 170 | */ | ||
| 171 | template<class T> | ||
| 172 | inline constexpr bool isRotationalExtrusion = false; | ||
| 173 | |||
| 174 | /*! | ||
| 175 | * \brief Convenience trait to check whether the extrusion is rotational | ||
| 176 | */ | ||
| 177 | template<int radialAxis> | ||
| 178 | inline constexpr bool isRotationalExtrusion<RotationalExtrusion<radialAxis>> = true; | ||
| 179 | |||
| 180 | } // end namespace Dumux | ||
| 181 | |||
| 182 | #endif | ||
| 183 |