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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 Fluidmatrixinteractions | ||
| 10 | * \brief A relationship for the porosity of a porous medium under mechanical deformation. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_MATERIAL_POROSITY_DEFORMATION_HH | ||
| 13 | #define DUMUX_MATERIAL_POROSITY_DEFORMATION_HH | ||
| 14 | |||
| 15 | #include <dumux/discretization/evalgradients.hh> | ||
| 16 | |||
| 17 | namespace Dumux { | ||
| 18 | |||
| 19 | /*! | ||
| 20 | * \ingroup Fluidmatrixinteractions | ||
| 21 | * \brief A relationship for the porosity of a porous medium under mechanical deformation. | ||
| 22 | * | ||
| 23 | * \tparam Scalar The type used for scalar values | ||
| 24 | */ | ||
| 25 | template<class Scalar> | ||
| 26 | class PorosityDeformation | ||
| 27 | { | ||
| 28 | public: | ||
| 29 | /*! | ||
| 30 | * \brief Calculates the porosity at a position inside an element | ||
| 31 | * \note This assumes the primary variables to be organized such that | ||
| 32 | * the displacements in the different grid directions are stored | ||
| 33 | * in the first entries of the primary variable vector. | ||
| 34 | * | ||
| 35 | * \param gridGeometry The finite volume grid geometry | ||
| 36 | * \param element The finite element | ||
| 37 | * \param elemSol The element solution | ||
| 38 | * \param globalPos The global position (in the element) | ||
| 39 | * \param refPoro The solid matrix porosity without deformation | ||
| 40 | * \param minPoro A minimum porosity value | ||
| 41 | * \param maxPoro A maximum porosity value | ||
| 42 | * | ||
| 43 | * \note \cite han2003 ( https://doi.org/10.1016/S0920-4105(03)00047-0 ) | ||
| 44 | * provide a derivation for \f$\text{d} \phi = -(1 - \phi ) \text{d} \epsilon_v \f$. | ||
| 45 | * Here, \f$\epsilon_v\f$ is equal to \f$\nabla \cdot \mathbf{u}\f$. | ||
| 46 | * By using an initial porosity \f$\phi_0\f$ and assuming \f$ \epsilon_{v, 0} = 0 \f$, | ||
| 47 | * one obtains \f$\phi = \frac{\phi_0 - \nabla \cdot \mathbf{u}}{1 - \nabla \cdot \mathbf{u}}\f$, | ||
| 48 | * which is the formulation for the rock mechanics sign convention. Here we are | ||
| 49 | * using the continuum mechanics sign convention, thus, the final formula reads: | ||
| 50 | * \f$\phi = \frac{\phi_0 + \nabla \cdot \mathbf{u}}{1 + \nabla \cdot \mathbf{u}}\f$. | ||
| 51 | */ | ||
| 52 | template< class FVGridGeom, class ElemSol > | ||
| 53 | 5602020 | static Scalar evaluatePorosity(const FVGridGeom& gridGeometry, | |
| 54 | const typename FVGridGeom::GridView::template Codim<0>::Entity& element, | ||
| 55 | const typename FVGridGeom::GridView::template Codim<0>::Entity::Geometry::GlobalCoordinate& globalPos, | ||
| 56 | const ElemSol& elemSol, | ||
| 57 | Scalar refPoro, | ||
| 58 | Scalar minPoro = 0.0, | ||
| 59 | Scalar maxPoro = 1.0) | ||
| 60 | { | ||
| 61 | // compute divergence of displacement at the given position | ||
| 62 | 5602020 | Scalar divU = 0.0; | |
| 63 | 5602020 | const auto gradU = evalGradients(element, element.geometry(), gridGeometry, elemSol, globalPos); | |
| 64 |
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22339180 | for (int dir = 0; dir < FVGridGeom::GridView::dimension; ++dir) |
| 65 | 50211480 | divU += gradU[dir][dir]; | |
| 66 | |||
| 67 | using std::clamp; | ||
| 68 |
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5602020 | return clamp((refPoro+divU)/(1.0+divU), minPoro, maxPoro); |
| 69 | } | ||
| 70 | |||
| 71 | /*! | ||
| 72 | * \brief Calculates the porosity at a position inside an element | ||
| 73 | * \note This assumes the primary variables to be organized such that | ||
| 74 | * the displacements in the different grid directions are stored | ||
| 75 | * in the first entries of the primary variable vector. | ||
| 76 | * | ||
| 77 | * | ||
| 78 | * \param gridGeometry The finite volume grid geometry | ||
| 79 | * \param element The finite element | ||
| 80 | * \param elemSol The element solution | ||
| 81 | * \param scv The sub-control volume | ||
| 82 | * \param refPoro The solid matrix porosity without deformation | ||
| 83 | * \param minPoro A minimum porosity value | ||
| 84 | */ | ||
| 85 | template< class FVGridGeom, class ElemSol > | ||
| 86 | static Scalar evaluatePorosity(const FVGridGeom& gridGeometry, | ||
| 87 | const typename FVGridGeom::GridView::template Codim<0>::Entity& element, | ||
| 88 | const typename FVGridGeom::SubControlVolume& scv, | ||
| 89 | const ElemSol& elemSol, | ||
| 90 | Scalar refPoro, | ||
| 91 | Scalar minPoro = 0.0) | ||
| 92 | { | ||
| 93 | // evaluate the porosity at the scv center | ||
| 94 | 451680 | return evaluatePorosity(gridGeometry, element, scv.center(), elemSol, refPoro, minPoro); | |
| 95 | } | ||
| 96 | }; | ||
| 97 | |||
| 98 | } // namespace Dumux | ||
| 99 | |||
| 100 | #endif | ||
| 101 |