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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_NIKURADSE_HH | ||
| 14 | #define DUMUX_MATERIAL_FLUIDMATRIX_FRICTIONLAW_NIKURADSE_HH | ||
| 15 | |||
| 16 | /*! | ||
| 17 | * \file | ||
| 18 | * \ingroup FrictionLaws | ||
| 19 | * \brief Implementation of the friction law after Nikuradse. | ||
| 20 | */ | ||
| 21 | #include <algorithm> | ||
| 22 | #include <cmath> | ||
| 23 | #include <dune/common/math.hh> | ||
| 24 | #include "frictionlaw.hh" | ||
| 25 | |||
| 26 | namespace Dumux { | ||
| 27 | /*! | ||
| 28 | * \addtogroup FrictionLaws | ||
| 29 | * \copydetails Dumux::FrictionLawNikuradse | ||
| 30 | */ | ||
| 31 | |||
| 32 | /*! | ||
| 33 | * \ingroup FrictionLaws | ||
| 34 | * \brief Implementation of the friction law after Nikuradse. | ||
| 35 | * | ||
| 36 | * ### Nikuradse | ||
| 37 | * | ||
| 38 | * This friction law calculates the stress between the flowing fluid and the bottom, | ||
| 39 | * which is called bottom shear stress, using the Nikuradse \cite Nikuradse1950 friction law | ||
| 40 | * | ||
| 41 | *\f$\tau_{x} = \frac{\kappa^2}{(ln\frac{12h}{ks})^2} u \sqrt{u^2 + v^2}\f$ and | ||
| 42 | *\f$\tau_{y} = \frac{\kappa^2}{(ln\frac{12h}{ks})^2} v \sqrt{u^2 + v^2}\f$ | ||
| 43 | * | ||
| 44 | * with the dimensionless Karman's constant \f$\mathrm{\kappa}\f$, the quivalent sand roughness | ||
| 45 | * \f$\mathrm{ks}\f$ in \f$\mathrm{[m]}\f$ and the water depth \f$\mathrm{h}\f$ | ||
| 46 | * in \f$\mathrm{[m]}\f$. | ||
| 47 | * | ||
| 48 | * The bottom shear stress is needed to calculate on the one hand the loss of | ||
| 49 | * momentum due to bottom friction and on the other hand the bedload transport rate. | ||
| 50 | * | ||
| 51 | * The LET mobility model is used to limit the friction for small water | ||
| 52 | * depths if a roughness height > 0.0 is provided (default roughnessHeight = 0.0). | ||
| 53 | * | ||
| 54 | */ | ||
| 55 | |||
| 56 | template <typename VolumeVariables> | ||
| 57 | class FrictionLawNikuradse : public FrictionLaw<VolumeVariables> | ||
| 58 | { | ||
| 59 | using Scalar = typename VolumeVariables::PrimaryVariables::value_type; | ||
| 60 | public: | ||
| 61 | /*! | ||
| 62 | * \brief Constructor | ||
| 63 | * | ||
| 64 | * \param ks Equivalent sand roughness (in m) | ||
| 65 | * \param roughnessHeight roughness height (in m) default = 0.0 | ||
| 66 | */ | ||
| 67 | 1 | FrictionLawNikuradse(const Scalar ks, const Scalar roughnessHeight=0.0) | |
| 68 |
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1 | : ks_(ks), roughnessHeight_(roughnessHeight) {} |
| 69 | |||
| 70 | /*! | ||
| 71 | * \brief Compute the bottom shear stress. | ||
| 72 | * | ||
| 73 | * \param volVars Volume variables | ||
| 74 | * | ||
| 75 | * Compute the bottom shear stress due to bottom friction. | ||
| 76 | * The bottom shear stress is a projection of the shear stress tensor onto the river bed. | ||
| 77 | * It can therefore be represented by a (tangent) vector with two entries. | ||
| 78 | * | ||
| 79 | * \return shear stress in N/m^2. First entry is the x-component, the second the y-component. | ||
| 80 | */ | ||
| 81 | 1071465 | Dune::FieldVector<Scalar, 2> bottomShearStress(const VolumeVariables& volVars) const final | |
| 82 | { | ||
| 83 | using Dune::power; | ||
| 84 | using std::log; | ||
| 85 | using std::hypot; | ||
| 86 | |||
| 87 | 1071465 | Dune::FieldVector<Scalar, 2> shearStress(0.0); | |
| 88 | |||
| 89 |
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1071465 | const Scalar artificialWaterDepth = this->limitRoughH(roughnessHeight_, volVars.waterDepth()); |
| 90 | 1071465 | const Scalar karmanConstant = 0.41; // Karman's constant is dimensionless | |
| 91 | 1071465 | const Scalar dimensionlessFactor = power(karmanConstant, 2)/power(log((12*(volVars.waterDepth() + artificialWaterDepth))/ks_), 2); | |
| 92 | 1071465 | const Scalar uv = hypot(volVars.velocity(0),volVars.velocity(1)); | |
| 93 | |||
| 94 | 1071465 | shearStress[0] = dimensionlessFactor * volVars.velocity(0) * uv * volVars.density(); | |
| 95 | 1071465 | shearStress[1] = dimensionlessFactor * volVars.velocity(1) * uv * volVars.density(); | |
| 96 | |||
| 97 | 1071465 | return shearStress; | |
| 98 | } | ||
| 99 | |||
| 100 | private: | ||
| 101 | Scalar ks_; | ||
| 102 | Scalar roughnessHeight_; | ||
| 103 | }; | ||
| 104 | |||
| 105 | } // end namespace Dumux | ||
| 106 | |||
| 107 | #endif | ||
| 108 |