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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 ShallowWaterModels | ||
| 10 | * \brief Compute boundary conditions for the Riemann Solver | ||
| 11 | * | ||
| 12 | * The boundary conditions are given at the the outer face of the | ||
| 13 | * the boundary cells. In this form the boundary condition can't be | ||
| 14 | * processed by the riemann Solver, because it needs two cell states, one at | ||
| 15 | * each side of a face. Therefore the Riemann invariants are used to | ||
| 16 | * calculate a virtual outer state. | ||
| 17 | */ | ||
| 18 | #ifndef DUMUX_SHALLOWWATER_BOUNDARYFLUXES_HH | ||
| 19 | #define DUMUX_SHALLOWWATER_BOUNDARYFLUXES_HH | ||
| 20 | |||
| 21 | #include <array> | ||
| 22 | #include <cmath> | ||
| 23 | #include <algorithm> | ||
| 24 | |||
| 25 | namespace Dumux::ShallowWater { | ||
| 26 | |||
| 27 | /*! | ||
| 28 | * \brief Compute the outer cell state for fixed water depth boundary. | ||
| 29 | * | ||
| 30 | * \param waterDepthBoundary Water depth at the boundary face [m^2/s] | ||
| 31 | * \param waterDepthInside Water depth in the inner cell [m] | ||
| 32 | * \param velocityXInside Velocity in x-direction in the inner cell [m/s] | ||
| 33 | * \param velocityYInside Velocity in y-direction in the inner cell [m/s] | ||
| 34 | * \param gravity Gravity constant [m/s^2] | ||
| 35 | * \param nxy Normal vector of the boundary face | ||
| 36 | * | ||
| 37 | * \return cellStateOutside The outer cell state | ||
| 38 | */ | ||
| 39 | template<class Scalar, class GlobalPosition> | ||
| 40 | 23418 | std::array<Scalar, 3> fixedWaterDepthBoundary(const Scalar waterDepthBoundary, | |
| 41 | const Scalar waterDepthInside, | ||
| 42 | const Scalar velocityXInside, | ||
| 43 | const Scalar velocityYInside, | ||
| 44 | const Scalar gravity, | ||
| 45 | const GlobalPosition& nxy) | ||
| 46 | |||
| 47 | { | ||
| 48 | std::array<Scalar, 3> cellStateOutside; | ||
| 49 | 46836 | cellStateOutside[0] = waterDepthBoundary; | |
| 50 | |||
| 51 | using std::sqrt; | ||
| 52 | 70254 | const auto uboundIn = nxy[0] * velocityXInside + nxy[1] * velocityYInside; | |
| 53 | 46836 | const auto uboundQut = uboundIn + 2.0 * sqrt(gravity * waterDepthInside) - 2.0 * sqrt(gravity * cellStateOutside[0]); | |
| 54 | |||
| 55 | 70254 | cellStateOutside[1] = (nxy[0] * uboundQut); // we only use the normal part | |
| 56 | 70254 | cellStateOutside[2] = (nxy[1] * uboundQut); // we only use the normal part | |
| 57 | |||
| 58 | 23418 | return cellStateOutside; | |
| 59 | } | ||
| 60 | |||
| 61 | /*! | ||
| 62 | * \brief Compute the outer cell state for a fixed discharge boundary. | ||
| 63 | * | ||
| 64 | * \param dischargeBoundary Discharge per meter at the boundary face [m^2/s] | ||
| 65 | * \param waterDepthInside Water depth in the inner cell [m] | ||
| 66 | * \param velocityXInside Velocity in x-direction in the inner cell [m/s] | ||
| 67 | * \param velocityYInside Velocity in y-direction in the inner cell [m/s] | ||
| 68 | * \param gravity Gravity constant [m/s^2] | ||
| 69 | * \param nxy Normal vector of the boundary face | ||
| 70 | * | ||
| 71 | * \return cellStateOutside The outer cell state | ||
| 72 | */ | ||
| 73 | template<class Scalar, class GlobalPosition> | ||
| 74 | 23143 | std::array<Scalar, 3> fixedDischargeBoundary(const Scalar dischargeBoundary, | |
| 75 | const Scalar waterDepthInside, | ||
| 76 | const Scalar velocityXInside, | ||
| 77 | const Scalar velocityYInside, | ||
| 78 | const Scalar gravity, | ||
| 79 | const GlobalPosition& nxy) | ||
| 80 | { | ||
| 81 | std::array<Scalar, 3> cellStateOutside; | ||
| 82 | using std::abs; | ||
| 83 | using std::sqrt; | ||
| 84 | using std::max; | ||
| 85 | |||
| 86 | // only impose if abs(q) > 0 | ||
| 87 |
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46286 | if (abs(dischargeBoundary) > 1.0e-9) |
| 88 | { | ||
| 89 | 46286 | const auto uboundIn = nxy[0]*velocityXInside + nxy[1]*velocityYInside; | |
| 90 | 23143 | const auto alphal = uboundIn + 2.0*sqrt(gravity * waterDepthInside); | |
| 91 | |||
| 92 | //initial guess for hstar solved with newton | ||
| 93 | 23143 | constexpr Scalar tol_hstar = 1.0E-12; | |
| 94 | 23143 | constexpr Scalar ink_hstar = 1.0E-9; | |
| 95 | 23143 | constexpr int maxstep_hstar = 30; | |
| 96 | |||
| 97 | 23143 | Scalar hstar = 0.1; | |
| 98 |
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228064 | for (int i = 0; i < maxstep_hstar; ++i) |
| 99 | { | ||
| 100 | 228064 | Scalar f_hstar = alphal - dischargeBoundary/hstar - 2 * sqrt(gravity * hstar); | |
| 101 | 228064 | Scalar df_hstar = (f_hstar -(alphal - dischargeBoundary/(hstar + ink_hstar) - 2 * sqrt(gravity * (hstar+ink_hstar))))/ink_hstar; | |
| 102 | 228064 | Scalar dx_hstar = -f_hstar/df_hstar; | |
| 103 |
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228064 | hstar = max(hstar - dx_hstar,0.001); |
| 104 | |||
| 105 |
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228064 | if (dx_hstar*dx_hstar < tol_hstar) |
| 106 | break; | ||
| 107 | } | ||
| 108 | |||
| 109 | 46286 | const auto qinner = (nxy[0] * waterDepthInside * velocityYInside) - (nxy[1] * waterDepthInside * velocityXInside); | |
| 110 | 23143 | cellStateOutside[0] = hstar; | |
| 111 | 69429 | cellStateOutside[1] = (nxy[0] * dischargeBoundary - nxy[1] * qinner)/hstar; | |
| 112 | 92572 | cellStateOutside[2] = (nxy[1] * dischargeBoundary + nxy[0] * qinner)/hstar; | |
| 113 | } | ||
| 114 | |||
| 115 | 23143 | return cellStateOutside; | |
| 116 | } | ||
| 117 | |||
| 118 | /*! | ||
| 119 | * \brief Compute the viscosity/diffusive flux at a rough wall boundary using no-slip formulation. | ||
| 120 | * | ||
| 121 | * \param alphaWall Roughness parameter: alphaWall=0.0 means full slip, alphaWall=1.0 means no slip, \f$0.0<\text{alphaWall}<1.0\f$ means partial slip [-] | ||
| 122 | * \param turbulentViscosity Turbulent viscosity [m^2/s] | ||
| 123 | * \param state Primary variables (water depth, velocities) | ||
| 124 | * \param cellCenterToBoundaryFaceCenter Cell-center to boundary distance | ||
| 125 | * \param unitNormal Normal vector of the boundary face | ||
| 126 | */ | ||
| 127 | template<class PrimaryVariables, class Scalar, class GlobalPosition> | ||
| 128 | 80173 | std::array<Scalar, 3> noslipWallBoundary(const Scalar alphaWall, | |
| 129 | const Scalar turbulentViscosity, | ||
| 130 | const PrimaryVariables& state, | ||
| 131 | const GlobalPosition& cellCenterToBoundaryFaceCenter, | ||
| 132 | const GlobalPosition& unitNormal) | ||
| 133 | { | ||
| 134 | // only impose if abs(alphaWall) > 0 | ||
| 135 | using std::abs; | ||
| 136 |
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160346 | if (abs(alphaWall) <= 1.0e-9) |
| 137 | ✗ | return {}; | |
| 138 | |||
| 139 |
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80173 | const auto waterDepth = state[0]; |
| 140 | // regularization: Set gradients to zero for drying cell | ||
| 141 | // Use LET-limiter instead for differentiability? | ||
| 142 |
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80173 | if (waterDepth <= 0.001) |
| 143 | ✗ | return {}; | |
| 144 | |||
| 145 | 80173 | const auto xVelocity = state[1]; | |
| 146 | 80173 | const auto yVelocity = state[2]; | |
| 147 | 80173 | const auto distance = cellCenterToBoundaryFaceCenter.two_norm(); | |
| 148 | |||
| 149 | // Compute the velocity gradients | ||
| 150 | // Outside - inside cell: therefore the minus-sign | ||
| 151 | // Only when cell contains sufficient water. | ||
| 152 | 80173 | const auto gradU = -alphaWall * xVelocity/distance; | |
| 153 | 80173 | const auto gradV = -alphaWall * yVelocity/distance; | |
| 154 | |||
| 155 | // Factor that takes the direction of the unit vector into account | ||
| 156 | 80173 | const auto direction = (unitNormal*cellCenterToBoundaryFaceCenter)/distance; | |
| 157 | |||
| 158 | // Compute the viscosity/diffusive fluxes at the rough wall | ||
| 159 | return { | ||
| 160 | 0.0, | ||
| 161 | 80173 | -turbulentViscosity*waterDepth*gradU*direction, | |
| 162 | 80173 | -turbulentViscosity*waterDepth*gradV*direction | |
| 163 | 80173 | }; | |
| 164 | } | ||
| 165 | |||
| 166 | /*! | ||
| 167 | * \brief Compute the viscosity/diffusive flux at a rough wall boundary using Nikuradse formulation. | ||
| 168 | * | ||
| 169 | * \param ksWall Nikuradse roughness height for the wall [m] | ||
| 170 | * \param state the primary variable state (water depth, velocities) | ||
| 171 | * \param cellCenterToBoundaryFaceCenter Cell-center to boundary distance | ||
| 172 | * \param unitNormal Normal vector of the boundary face | ||
| 173 | */ | ||
| 174 | template<class PrimaryVariables, class Scalar, class GlobalPosition> | ||
| 175 | ✗ | std::array<Scalar, 3> nikuradseWallBoundary(const Scalar ksWall, | |
| 176 | const PrimaryVariables& state, | ||
| 177 | const GlobalPosition& cellCenterToBoundaryFaceCenter, | ||
| 178 | const GlobalPosition& unitNormal) | ||
| 179 | { | ||
| 180 | // only impose if abs(ksWall) > 0 | ||
| 181 | using std::abs; | ||
| 182 | ✗ | if (abs(ksWall) <= 1.0e-9) | |
| 183 | ✗ | return {}; | |
| 184 | |||
| 185 | using std::hypot; | ||
| 186 | ✗ | const Scalar xVelocity = state[1]; | |
| 187 | ✗ | const Scalar yVelocity = state[2]; | |
| 188 | ✗ | const Scalar velocityMagnitude = hypot(xVelocity, yVelocity); | |
| 189 | ✗ | const Scalar distance = cellCenterToBoundaryFaceCenter.two_norm(); | |
| 190 | ✗ | const Scalar y0w = ksWall/30.0; | |
| 191 | ✗ | constexpr Scalar kappa2 = 0.41*0.41; | |
| 192 | |||
| 193 | // should distance/y0w be limited to not become too small? | ||
| 194 | using std::log; using std::max; | ||
| 195 | ✗ | const auto logYPlus = log(distance/y0w+1.0); | |
| 196 | ✗ | const auto fac = kappa2*velocityMagnitude / max(1.0e-3,logYPlus*logYPlus); | |
| 197 | |||
| 198 | // Factor that takes the direction of the unit vector into account | ||
| 199 | ✗ | const auto direction = (unitNormal*cellCenterToBoundaryFaceCenter)/distance; | |
| 200 | |||
| 201 | // wall shear stress vector | ||
| 202 | ✗ | const auto tauWx = direction*fac*xVelocity; | |
| 203 | ✗ | const auto tauWy = direction*fac*yVelocity; | |
| 204 | |||
| 205 | // Compute the viscosity/diffusive fluxes at the rough wall | ||
| 206 | ✗ | const auto waterDepth = state[0]; | |
| 207 | ✗ | return {0.0, waterDepth*tauWx, waterDepth*tauWy}; | |
| 208 | } | ||
| 209 | |||
| 210 | } // end namespace Dumux::ShallowWater | ||
| 211 | |||
| 212 | #endif | ||
| 213 |