| 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-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 friction law after Manning. | ||
| 11 | */ | ||
| 12 | |||
| 13 | #ifndef DUMUX_MATERIAL_FLUIDMATRIX_FRICTIONLAW_MANNING_HH | ||
| 14 | #define DUMUX_MATERIAL_FLUIDMATRIX_FRICTIONLAW_MANNING_HH | ||
| 15 | |||
| 16 | #include <algorithm> | ||
| 17 | #include <cmath> | ||
| 18 | #include <dune/common/math.hh> | ||
| 19 | #include "frictionlaw.hh" | ||
| 20 | |||
| 21 | namespace Dumux { | ||
| 22 | /*! | ||
| 23 | * \addtogroup FrictionLaws | ||
| 24 | * \copydetails Dumux::FrictionLawManning | ||
| 25 | */ | ||
| 26 | |||
| 27 | /*! | ||
| 28 | * \ingroup FrictionLaws | ||
| 29 | * \brief Implementation of the friction law after Manning. | ||
| 30 | * | ||
| 31 | * ### Manning | ||
| 32 | * | ||
| 33 | * This friction law calculates the stress between the flowing fluid and the bottom, | ||
| 34 | * which is called bottom shear stress, using the Manning friction law: | ||
| 35 | * | ||
| 36 | * \f$\tau_{x} = \frac{g}{(\frac{h^{1/6}}{n})^2} u \sqrt{u^2 + v^2}\f$ and | ||
| 37 | * \f$\tau_{y} = \frac{g}{(\frac{h^{1/6}}{n})^2} v \sqrt{u^2 + v^2}\f$ | ||
| 38 | * | ||
| 39 | * with the gravity constant \f$\mathrm{g}\f$ in \f$\mathrm{[m/s^2]}\f$, the water depth | ||
| 40 | * \f$\mathrm{h}\f$ in \f$\mathrm{[m]}\f$ and the Manning friction coefficient | ||
| 41 | * \f$\mathrm{n}\f$ in \f$\mathrm{[s/m^{1/3}]}\f$. | ||
| 42 | * | ||
| 43 | * The bottom shear stress is needed to calculate on the one hand the loss of | ||
| 44 | * momentum due to bottom friction and on the other hand the bedload transport rate. | ||
| 45 | * | ||
| 46 | * The LET mobility model is used to limit the friction for small water | ||
| 47 | * depths if a roughness height > 0.0 is provided (default roughnessHeight = 0.0). | ||
| 48 | */ | ||
| 49 | |||
| 50 | template <typename VolumeVariables> | ||
| 51 | class FrictionLawManning : public FrictionLaw<VolumeVariables> | ||
| 52 | { | ||
| 53 | using Scalar = typename VolumeVariables::PrimaryVariables::value_type; | ||
| 54 | public: | ||
| 55 | /*! | ||
| 56 | * \brief Constructor | ||
| 57 | * | ||
| 58 | * \param gravity Gravity constant (in m/s^2) | ||
| 59 | * \param manningN Manning friction coefficient (in s/m^(1/3) | ||
| 60 | * \param roughnessHeight roughness height for limiting (in m) default = 0.0 | ||
| 61 | */ | ||
| 62 | 2 | FrictionLawManning(const Scalar gravity, const Scalar manningN, const Scalar roughnessHeight=0.0) | |
| 63 |
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2 | : gravity_(gravity), manningN_(manningN), roughnessHeight_(roughnessHeight) {} |
| 64 | |||
| 65 | /*! | ||
| 66 | * \brief Compute the bottom shear stress. | ||
| 67 | * | ||
| 68 | * \param volVars Volume variables | ||
| 69 | * | ||
| 70 | * Compute the bottom shear stress due to bottom friction. | ||
| 71 | * The bottom shear stress is a projection of the shear stress tensor onto the river bed. | ||
| 72 | * It can therefore be represented by a (tangent) vector with two entries. | ||
| 73 | * | ||
| 74 | * \return shear stress in N/m^2. First entry is the x-component, the second the y-component. | ||
| 75 | */ | ||
| 76 | 1378282 | Dune::FieldVector<Scalar, 2> bottomShearStress(const VolumeVariables& volVars) const final | |
| 77 | { | ||
| 78 | using std::pow; | ||
| 79 | using Dune::power; | ||
| 80 | using std::hypot; | ||
| 81 | |||
| 82 | 1378282 | Dune::FieldVector<Scalar, 2> shearStress(0.0); | |
| 83 | |||
| 84 |
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1378282 | const Scalar artificialWaterDepth = this->limitRoughH(roughnessHeight_, volVars.waterDepth()); |
| 85 | // c has units of m^(1/2)/s so c^2 has units of m/s^2 | ||
| 86 | 1378282 | const Scalar c = pow(volVars.waterDepth() + artificialWaterDepth, 1.0/6.0) * 1.0/(manningN_); | |
| 87 | 1378282 | const Scalar uv = hypot(volVars.velocity(0), volVars.velocity(1)); | |
| 88 | 1378282 | const Scalar dimensionlessFactor = gravity_/(c*c); | |
| 89 | |||
| 90 | 1378282 | shearStress[0] = dimensionlessFactor * volVars.velocity(0) * uv * volVars.density(); | |
| 91 | 1378282 | shearStress[1] = dimensionlessFactor * volVars.velocity(1) * uv * volVars.density(); | |
| 92 | |||
| 93 | 1378282 | return shearStress; | |
| 94 | } | ||
| 95 | |||
| 96 | private: | ||
| 97 | Scalar gravity_; | ||
| 98 | Scalar manningN_; | ||
| 99 | Scalar roughnessHeight_; | ||
| 100 | }; | ||
| 101 | |||
| 102 | } // end namespace Dumux | ||
| 103 | |||
| 104 | #endif | ||
| 105 |