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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-FileCopyrightText: 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 FrictionLaws | ||
| 10 | * \brief Implementation of the abstract base class for friction laws. | ||
| 11 | */ | ||
| 12 | |||
| 13 | #ifndef DUMUX_MATERIAL_FLUIDMATRIX_FRICTIONLAW_HH | ||
| 14 | #define DUMUX_MATERIAL_FLUIDMATRIX_FRICTIONLAW_HH | ||
| 15 | |||
| 16 | #include <algorithm> | ||
| 17 | #include <cmath> | ||
| 18 | |||
| 19 | #include <dune/common/fvector.hh> | ||
| 20 | |||
| 21 | namespace Dumux { | ||
| 22 | |||
| 23 | /*! | ||
| 24 | * \ingroup FrictionLaws | ||
| 25 | * \brief Implementation of the abstract base class for friction laws. | ||
| 26 | * | ||
| 27 | * A LET mobility model of Lomeland et al. 2005 \cite Lomeland2005 can be used to add an | ||
| 28 | * artificial water depth to limit the friction for small water depths. | ||
| 29 | * | ||
| 30 | * \note Instead of calculating the bed friction term \f$\mathbf{S_f}\f$ | ||
| 31 | * of the shallow water equations, the implemented friction laws | ||
| 32 | * calculate the shear stress \f$\tau_{x}\f$ and \f$\tau_{y}\f$. | ||
| 33 | */ | ||
| 34 | |||
| 35 | template <typename VolumeVariables > | ||
| 36 |
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7 | class FrictionLaw |
| 37 | { | ||
| 38 | using Scalar = typename VolumeVariables::PrimaryVariables::value_type; | ||
| 39 | public: | ||
| 40 | /*! | ||
| 41 | * \brief Compute the bottom shear stress. | ||
| 42 | * | ||
| 43 | * \param volVars Volume variables | ||
| 44 | * | ||
| 45 | * Compute the bottom shear stress due to bottom friction. | ||
| 46 | * The bottom shear stress is a projection of the shear stress tensor onto the river bed. | ||
| 47 | * It can therefore be represented by a (tangent) vector with two entries. | ||
| 48 | * | ||
| 49 | * \return shear stress [N/m^2]. First entry is the x-component, the second the y-component. | ||
| 50 | */ | ||
| 51 | virtual Dune::FieldVector<Scalar, 2> bottomShearStress(const VolumeVariables& volVars) const = 0; | ||
| 52 | |||
| 53 | /*! | ||
| 54 | * \brief Limit the friction for small water depth. | ||
| 55 | * | ||
| 56 | * Compute a small artificial water depth that is added to the | ||
| 57 | * actual water depth to avoid extreme friction values which can | ||
| 58 | * occur for small water depths. | ||
| 59 | * | ||
| 60 | * The function is called with a roughness height, which can be | ||
| 61 | * seen as roughness height of the surface (e.g. grain size). For a | ||
| 62 | * zero roughnessHeight the artificial water depth will be zero. | ||
| 63 | * | ||
| 64 | * A water depth minUpperH (minUpperH = 2 * roughnessHeight) is | ||
| 65 | * defined for the limiting. Limiting is applied between both | ||
| 66 | * depths. | ||
| 67 | * | ||
| 68 | * ------------------------- minUpperH ----------- | ||
| 69 | * | ||
| 70 | * | ||
| 71 | * | ||
| 72 | * ------------------------roughnessHeight --------------- | ||
| 73 | * /\ /\ roughness /grain\ | ||
| 74 | * -------------------------------bottom ------------------ | ||
| 75 | * ///////////////////////////////////////////////// | ||
| 76 | * | ||
| 77 | * For the limiting the LET model is used, which is usually applied in the | ||
| 78 | * porous media flow to limit the permeability due to the saturation. It employs | ||
| 79 | * the three empirical parameters L, E and T, which describe the limiting curve (mobility). | ||
| 80 | * | ||
| 81 | * auto mobility = (mobility_max * pow(sw,L))/(pow(sw,L) + E * pow(1.0-sw,T)); | ||
| 82 | * | ||
| 83 | * For the limitation of the roughness height L = 0.0, T = 2.0 and E = 1.0 are chosen. | ||
| 84 | * Therefore the calculation of the mobility is simplified significantly. | ||
| 85 | * | ||
| 86 | * \param roughnessHeight roughness height of the representative structure (e.g. largest grain size). | ||
| 87 | * \param waterDepth water depth. | ||
| 88 | * \param eps If the roughness height falls below this threshold, this function returns zero. | ||
| 89 | */ | ||
| 90 | 2449747 | Scalar limitRoughH(const Scalar roughnessHeight, const Scalar waterDepth, const Scalar eps=1.0e-12) const | |
| 91 | { | ||
| 92 | using std::clamp; | ||
| 93 | |||
| 94 | // return zero if the roughness depth is near zero | ||
| 95 |
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2449747 | if (roughnessHeight < eps) return 0.0; |
| 96 | |||
| 97 | // calculate the artificial water depth | ||
| 98 | 1071465 | const Scalar mobilityMax = 1.0; //!< maximal mobility | |
| 99 | |||
| 100 | 1071465 | const Scalar minUpperH = roughnessHeight * 2.0; | |
| 101 |
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1071465 | const Scalar sw = clamp(waterDepth * (1.0/minUpperH), 0.0, 1.0); |
| 102 | 1071465 | const Scalar mobility = mobilityMax /(1.0 + (1.0-sw)*(1.0-sw)); | |
| 103 | 1071465 | return roughnessHeight * (1.0 - mobility); | |
| 104 | } | ||
| 105 | |||
| 106 | // virtual base class needs a virtual destructor | ||
| 107 | virtual ~FrictionLaw() = default; | ||
| 108 | }; | ||
| 109 | |||
| 110 | } // end namespace Dumux | ||
| 111 | |||
| 112 | #endif | ||
| 113 |