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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 NavierStokesModel | ||
| 10 | * \copydoc Dumux::StaggeredVelocityGradients | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_NAVIERSTOKES_STAGGERED_VELOCITYGRADIENTS_HH | ||
| 13 | #define DUMUX_NAVIERSTOKES_STAGGERED_VELOCITYGRADIENTS_HH | ||
| 14 | |||
| 15 | #include <optional> | ||
| 16 | #include <dumux/common/exceptions.hh> | ||
| 17 | #include <dumux/common/parameters.hh> | ||
| 18 | |||
| 19 | namespace Dumux { | ||
| 20 | |||
| 21 | /*! | ||
| 22 | * \ingroup NavierStokesModel | ||
| 23 | * \brief Helper class for calculating the velocity gradients for the Navier-Stokes model using the staggered grid discretization. | ||
| 24 | */ | ||
| 25 | template<class Scalar, class GridGeometry, class BoundaryTypes, class Indices> | ||
| 26 | class StaggeredVelocityGradients | ||
| 27 | { | ||
| 28 | using FVElementGeometry = typename GridGeometry::LocalView; | ||
| 29 | using GridView = typename GridGeometry::GridView; | ||
| 30 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 31 | using SubControlVolumeFace = typename FVElementGeometry::SubControlVolumeFace; | ||
| 32 | using GlobalPosition = typename Element::Geometry::GlobalCoordinate; | ||
| 33 | |||
| 34 | public: | ||
| 35 | |||
| 36 | /*! | ||
| 37 | * \brief Returns the in-axis velocity gradient. | ||
| 38 | * | ||
| 39 | * \verbatim | ||
| 40 | * ---------======= == and # staggered half-control-volume | ||
| 41 | * | # | current scvf | ||
| 42 | * | # | # staggered face over which fluxes are calculated | ||
| 43 | * vel.Opp <~~| O~~> x~~~~> vel.Self | ||
| 44 | * | # | x dof position | ||
| 45 | * scvf | # | | ||
| 46 | * --------======== -- element | ||
| 47 | * | ||
| 48 | * O position at which gradient is evaluated | ||
| 49 | * \endverbatim | ||
| 50 | */ | ||
| 51 | template<class FaceVariables> | ||
| 52 |
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145578344 | static Scalar velocityGradII(const SubControlVolumeFace& scvf, |
| 53 | const FaceVariables& faceVars) | ||
| 54 | { | ||
| 55 | // The velocities of the dof at interest and the one of the opposite scvf. | ||
| 56 |
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145578344 | const Scalar velocitySelf = faceVars.velocitySelf(); |
| 57 | 145578344 | const Scalar velocityOpposite = faceVars.velocityOpposite(); | |
| 58 | |||
| 59 |
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145578344 | return ((velocityOpposite - velocitySelf) / scvf.selfToOppositeDistance()) * scvf.directionSign(); |
| 60 | } | ||
| 61 | |||
| 62 | /*! | ||
| 63 | * \brief Returns the velocity gradient perpendicular to the orientation of our current scvf. | ||
| 64 | * | ||
| 65 | * \verbatim | ||
| 66 | * ---------------- | ||
| 67 | * | |vel. | ||
| 68 | * | |Parallel | ||
| 69 | * | |~~~~> -------> | ||
| 70 | * | | ------> * gradient | ||
| 71 | * | | -----> | ||
| 72 | * scvf ---------######O::::::::: ----> || and # staggered half-control-volume (own element) | ||
| 73 | * | || | curr. :: ---> | ||
| 74 | * | || | scvf :: --> :: staggered half-control-volume (neighbor element) | ||
| 75 | * | || x~~~~> :: -> | ||
| 76 | * | || | vel. :: # lateral staggered faces over which fluxes are calculated | ||
| 77 | * scvf | || | Self :: | ||
| 78 | * ---------#######::::::::: x dof position | ||
| 79 | * scvf | ||
| 80 | * -- elements | ||
| 81 | * | ||
| 82 | * O position at which gradient is evaluated | ||
| 83 | * \endverbatim | ||
| 84 | * | ||
| 85 | * ------------ | ||
| 86 | * | xxxx s | ||
| 87 | * | xxxx a | ||
| 88 | * | xxxx s | ||
| 89 | * -----------O----------- | ||
| 90 | * | yyyy s zzzz | | ||
| 91 | * | yyyy b zzzz | | ||
| 92 | * | yyyy s zzzz | | ||
| 93 | * ----------------------- | ||
| 94 | * | ||
| 95 | * In a corner geometry (scvf is sas or sbs), we calculate the velocity gradient at O, by | ||
| 96 | * (velocity(a)-velocity(b))/distance(a,b) for the half-control volumes x and y, but by | ||
| 97 | * (velocity(O)-velocity(b))/distance(O,b) for z. This does not harm flux continuity (x and y use the same | ||
| 98 | * formulation). We do this different formulation for y (approximate gradient by central differncing) and | ||
| 99 | * z (approximate gradient by forward/backward differencing), because it is the natural way of implementing | ||
| 100 | * it and it is not clear which gradient is the better approximation in this case anyway. | ||
| 101 | * Particularly, for the frequent case of no-slip, no-flow boundaries, the velocity would be zero at O and a | ||
| 102 | * and thus, the gradient within the flow domain might be better approximated by velocity(b)/distanc(O,b) | ||
| 103 | * than by velocity(b)/distance(a,b). | ||
| 104 | */ | ||
| 105 | template<class Problem, class FaceVariables> | ||
| 106 | 285829870 | static Scalar velocityGradIJ(const Problem& problem, | |
| 107 | const Element& element, | ||
| 108 | const FVElementGeometry& fvGeometry, | ||
| 109 | const SubControlVolumeFace& scvf, | ||
| 110 | const FaceVariables& faceVars, | ||
| 111 | const std::optional<BoundaryTypes>& currentScvfBoundaryTypes, | ||
| 112 | const std::optional<BoundaryTypes>& lateralFaceBoundaryTypes, | ||
| 113 | const std::size_t localSubFaceIdx) | ||
| 114 | { | ||
| 115 | 285829870 | const auto eIdx = scvf.insideScvIdx(); | |
| 116 | 285829870 | const auto& lateralScvf = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx); | |
| 117 | |||
| 118 | // For the velocityGrad_ij derivative, get the velocities at the current (own) scvf | ||
| 119 | // and at the parallel one at the neighboring scvf. | ||
| 120 | 285829870 | const Scalar innerParallelVelocity = faceVars.velocitySelf(); | |
| 121 | |||
| 122 | 857489610 | const auto outerParallelVelocity = [&]() | |
| 123 | { | ||
| 124 |
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285829870 | if (!lateralScvf.boundary()) |
| 125 | 276911036 | return faceVars.velocityParallel(localSubFaceIdx, 0); | |
| 126 |
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8918834 | else if (lateralFaceBoundaryTypes->isDirichlet(Indices::velocity(scvf.directionIndex()))) |
| 127 | { | ||
| 128 | // Sample the value of the Dirichlet BC at the center of the staggered lateral face. | ||
| 129 | 8663412 | const auto& lateralBoundaryFacePos = lateralStaggeredFaceCenter_(scvf, localSubFaceIdx); | |
| 130 | 17326824 | const auto lateralBoundaryFace = makeStaggeredBoundaryFace(lateralScvf, lateralBoundaryFacePos); | |
| 131 |
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8982176 | return problem.dirichlet(element, lateralBoundaryFace)[Indices::velocity(scvf.directionIndex())]; |
| 132 | 8663412 | } | |
| 133 |
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255422 | else if (lateralFaceBoundaryTypes->isBeaversJoseph(Indices::velocity(scvf.directionIndex()))) |
| 134 | { | ||
| 135 | 255422 | return beaversJosephVelocityAtLateralScvf(problem, element, fvGeometry, scvf, faceVars, | |
| 136 | 255422 | currentScvfBoundaryTypes, lateralFaceBoundaryTypes, localSubFaceIdx); | |
| 137 | } | ||
| 138 | else | ||
| 139 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid lateral boundary type at " << lateralScvf.center()); | |
| 140 | 285829870 | }(); | |
| 141 | |||
| 142 | // The velocity gradient already accounts for the orientation | ||
| 143 | // of the staggered face's outer normal vector. This also correctly accounts for the reduced | ||
| 144 | // distance used in the gradient if the lateral scvf lies on a boundary. | ||
| 145 | 285829870 | return (outerParallelVelocity - innerParallelVelocity) | |
| 146 | 285829870 | / scvf.parallelDofsDistance(localSubFaceIdx, 0) * lateralScvf.directionSign(); | |
| 147 | } | ||
| 148 | |||
| 149 | /*! | ||
| 150 | * \brief Returns the velocity gradient in line with our current scvf. | ||
| 151 | * | ||
| 152 | * \verbatim | ||
| 153 | * ^ gradient | ||
| 154 | * | ^ | ||
| 155 | * | | ^ | ||
| 156 | * | | | ^ | ||
| 157 | * | | | | ^ | ||
| 158 | * | | | | | ^ | ||
| 159 | * | | | | | | | ||
| 160 | * | ||
| 161 | * ---------------- | ||
| 162 | * | | | ||
| 163 | * | in.norm. | | ||
| 164 | * | vel. | | ||
| 165 | * | ^ | ^ out.norm.vel. | ||
| 166 | * | | | | | ||
| 167 | * scvf ---------######O::::::::: || and # staggered half-control-volume (own element) | ||
| 168 | * | || | curr. :: | ||
| 169 | * | || | scvf :: :: staggered half-control-volume (neighbor element) | ||
| 170 | * | || x~~~~> :: | ||
| 171 | * | || | vel. :: # lateral staggered faces over which fluxes are calculated | ||
| 172 | * scvf | || | Self :: | ||
| 173 | * ---------#######::::::::: x dof position | ||
| 174 | * scvf | ||
| 175 | * -- elements | ||
| 176 | * | ||
| 177 | * O position at which gradient is evaluated | ||
| 178 | * \endverbatim | ||
| 179 | */ | ||
| 180 | template<class Problem, class FaceVariables> | ||
| 181 |
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284898272 | static Scalar velocityGradJI(const Problem& problem, |
| 182 | const Element& element, | ||
| 183 | const FVElementGeometry& fvGeometry, | ||
| 184 | const SubControlVolumeFace& scvf, | ||
| 185 | const FaceVariables& faceVars, | ||
| 186 | const std::optional<BoundaryTypes>& currentScvfBoundaryTypes, | ||
| 187 | const std::optional<BoundaryTypes>& lateralFaceBoundaryTypes, | ||
| 188 | const std::size_t localSubFaceIdx) | ||
| 189 | { | ||
| 190 | 284898272 | const auto eIdx = scvf.insideScvIdx(); | |
| 191 |
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284898272 | const auto& lateralScvf = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx); |
| 192 | |||
| 193 | // Assume a zero velocity gradient for pressure boundary conditions. | ||
| 194 |
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284898272 | if (currentScvfBoundaryTypes && currentScvfBoundaryTypes->isDirichlet(Indices::pressureIdx)) |
| 195 | return 0.0; | ||
| 196 | |||
| 197 | // For the velocityGrad_ji gradient, get the velocities perpendicular to the velocity at the current scvf. | ||
| 198 | // The inner one is located at staggered face within the own element, | ||
| 199 | // the outer one at the respective staggered face of the element on the other side of the | ||
| 200 | // current scvf. | ||
| 201 | 284898272 | const Scalar innerLateralVelocity = faceVars.velocityLateralInside(localSubFaceIdx); | |
| 202 | 854694816 | const Scalar outerLateralVelocity = [&]() | |
| 203 | { | ||
| 204 |
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284898272 | if (!scvf.boundary()) |
| 205 | 284551500 | return faceVars.velocityLateralOutside(localSubFaceIdx); | |
| 206 |
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346772 | else if (currentScvfBoundaryTypes->isDirichlet(Indices::velocity(lateralScvf.directionIndex()))) |
| 207 | { | ||
| 208 | // Sample the value of the Dirichlet BC at the center of the lateral face intersecting with the boundary. | ||
| 209 | ✗ | const auto& lateralBoundaryFacePos = lateralStaggeredFaceCenter_(scvf, localSubFaceIdx); | |
| 210 | ✗ | const auto lateralBoundaryFace = makeStaggeredBoundaryFace(scvf, lateralBoundaryFacePos); | |
| 211 | ✗ | return problem.dirichlet(element, lateralBoundaryFace)[Indices::velocity(lateralScvf.directionIndex())]; | |
| 212 | ✗ | } | |
| 213 |
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346772 | else if (currentScvfBoundaryTypes->isBeaversJoseph(Indices::velocity(lateralScvf.directionIndex()))) |
| 214 | { | ||
| 215 | 346772 | return beaversJosephVelocityAtCurrentScvf(problem, element, fvGeometry, scvf, faceVars, | |
| 216 | 346772 | currentScvfBoundaryTypes, lateralFaceBoundaryTypes, localSubFaceIdx); | |
| 217 | } | ||
| 218 | else | ||
| 219 | ✗ | DUNE_THROW(Dune::InvalidStateException, "Invalid lateral boundary types at " << lateralScvf.center()); | |
| 220 |
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284898272 | }(); |
| 221 | |||
| 222 | // Calculate the velocity gradient in positive coordinate direction. | ||
| 223 | 569796544 | const Scalar lateralDeltaV = scvf.normalInPosCoordDir() | |
| 224 |
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284898272 | ? (outerLateralVelocity - innerLateralVelocity) |
| 225 | : (innerLateralVelocity - outerLateralVelocity); | ||
| 226 | |||
| 227 | 284898272 | return lateralDeltaV / scvf.pairData(localSubFaceIdx).lateralDistance; | |
| 228 | } | ||
| 229 | |||
| 230 | /*! | ||
| 231 | * \brief Returns the Beavers-Jospeh slip velocity for a scvf which lies on the boundary itself. | ||
| 232 | * | ||
| 233 | * \verbatim | ||
| 234 | * in.norm. B-J slip | ||
| 235 | * vel. vel. | ||
| 236 | * ^ ^ | ||
| 237 | * | | | ||
| 238 | * scvf ---------######|* * boundary | ||
| 239 | * | || |* curr. | ||
| 240 | * | || |* scvf || and # staggered half-control-volume (own element) | ||
| 241 | * | || x~~~~> | ||
| 242 | * | || |* vel. # lateral staggered faces | ||
| 243 | * scvf | || |* Self | ||
| 244 | * ---------#######* x dof position | ||
| 245 | * scvf | ||
| 246 | * -- element | ||
| 247 | * \endverbatim | ||
| 248 | * | ||
| 249 | */ | ||
| 250 | template<class Problem, class FaceVariables> | ||
| 251 | 496380 | static Scalar beaversJosephVelocityAtCurrentScvf(const Problem& problem, | |
| 252 | const Element& element, | ||
| 253 | const FVElementGeometry& fvGeometry, | ||
| 254 | const SubControlVolumeFace& scvf, | ||
| 255 | const FaceVariables& faceVars, | ||
| 256 | const std::optional<BoundaryTypes>& currentScvfBoundaryTypes, | ||
| 257 | const std::optional<BoundaryTypes>& lateralFaceBoundaryTypes, | ||
| 258 | const std::size_t localSubFaceIdx) | ||
| 259 | { | ||
| 260 | 496380 | const auto eIdx = scvf.insideScvIdx(); | |
| 261 | 496380 | const auto& lateralScvf = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx); | |
| 262 | 496380 | const Scalar innerLateralVelocity = faceVars.velocityLateralInside(localSubFaceIdx); | |
| 263 | |||
| 264 | 1489140 | const auto tangentialVelocityGradient = [&]() | |
| 265 | { | ||
| 266 | // If the current scvf is on a boundary and if a Dirichlet BC for the pressure or a BJ condition for | ||
| 267 | // the slip velocity is set there, assume a tangential velocity gradient of zero along the lateral face | ||
| 268 | // (towards the current scvf). | ||
| 269 |
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496397 | static const bool unsymmetrizedGradientForBJ = getParamFromGroup<bool>(problem.paramGroup(), |
| 270 |
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34 | "FreeFlow.EnableUnsymmetrizedVelocityGradientForBeaversJoseph", false); |
| 271 | |||
| 272 |
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496380 | if (unsymmetrizedGradientForBJ) |
| 273 | return 0.0; | ||
| 274 | |||
| 275 |
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429420 | if (lateralScvf.boundary()) |
| 276 | { | ||
| 277 |
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509881 | if (lateralFaceBoundaryTypes->isDirichlet(Indices::pressureIdx) || |
| 278 |
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13501 | lateralFaceBoundaryTypes->isBeaversJoseph(Indices::velocity(scvf.directionIndex()))) |
| 279 | return 0.0; | ||
| 280 | } | ||
| 281 | |||
| 282 | 420169 | return velocityGradIJ(problem, element, fvGeometry, scvf, faceVars, currentScvfBoundaryTypes, lateralFaceBoundaryTypes, localSubFaceIdx); | |
| 283 | 496380 | }(); | |
| 284 | |||
| 285 | 496380 | return problem.beaversJosephVelocity(element, | |
| 286 | 496380 | fvGeometry.scv(scvf.insideScvIdx()), | |
| 287 | lateralScvf, | ||
| 288 | scvf, /*on boundary*/ | ||
| 289 | innerLateralVelocity, | ||
| 290 | 496380 | tangentialVelocityGradient); | |
| 291 | } | ||
| 292 | |||
| 293 | /*! | ||
| 294 | * \brief Returns the Beavers-Jospeh slip velocity for a lateral scvf which lies on the boundary. | ||
| 295 | * | ||
| 296 | * \verbatim | ||
| 297 | * B-J slip * boundary | ||
| 298 | * ************** vel. ***** | ||
| 299 | * scvf ---------##### ~~~~> :::: || and # staggered half-control-volume (own element) | ||
| 300 | * | || | curr. :: | ||
| 301 | * | || | scvf :: :: staggered half-control-volume (neighbor element) | ||
| 302 | * | || x~~~~> :: | ||
| 303 | * | || | vel. :: # lateral staggered faces | ||
| 304 | * scvf | || | Self :: | ||
| 305 | * ---------#######::::::::: x dof position | ||
| 306 | * scvf | ||
| 307 | * -- elements | ||
| 308 | * \endverbatim | ||
| 309 | */ | ||
| 310 | template<class Problem, class FaceVariables> | ||
| 311 | 367330 | static Scalar beaversJosephVelocityAtLateralScvf(const Problem& problem, | |
| 312 | const Element& element, | ||
| 313 | const FVElementGeometry& fvGeometry, | ||
| 314 | const SubControlVolumeFace& scvf, | ||
| 315 | const FaceVariables& faceVars, | ||
| 316 | const std::optional<BoundaryTypes>& currentScvfBoundaryTypes, | ||
| 317 | const std::optional<BoundaryTypes>& lateralFaceBoundaryTypes, | ||
| 318 | const std::size_t localSubFaceIdx) | ||
| 319 | { | ||
| 320 | 367330 | const auto eIdx = scvf.insideScvIdx(); | |
| 321 | 367330 | const auto& lateralScvf = fvGeometry.scvf(eIdx, scvf.pairData(localSubFaceIdx).localLateralFaceIdx); | |
| 322 | 367330 | const Scalar innerParallelVelocity = faceVars.velocitySelf(); | |
| 323 | |||
| 324 | 1101990 | const auto tangentialVelocityGradient = [&]() | |
| 325 | { | ||
| 326 | // If the current scvf is on a boundary and if a Dirichlet BC for the pressure or a BJ condition for | ||
| 327 | // the slip velocity is set there, assume a tangential velocity gradient of zero along the lateral face | ||
| 328 | // (towards the current scvf). | ||
| 329 |
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367347 | static const bool unsymmetrizedGradientForBJ = getParamFromGroup<bool>(problem.paramGroup(), |
| 330 |
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34 | "FreeFlow.EnableUnsymmetrizedVelocityGradientForBeaversJoseph", false); |
| 331 | |||
| 332 |
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367330 | if (unsymmetrizedGradientForBJ) |
| 333 | return 0.0; | ||
| 334 | |||
| 335 |
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311930 | if (scvf.boundary()) |
| 336 | { | ||
| 337 |
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367330 | if (currentScvfBoundaryTypes->isDirichlet(Indices::pressureIdx) || |
| 338 | ✗ | currentScvfBoundaryTypes->isBeaversJoseph(Indices::velocity(lateralScvf.directionIndex()))) | |
| 339 | return 0.0; | ||
| 340 | } | ||
| 341 | |||
| 342 | 304892 | return velocityGradJI(problem, element, fvGeometry, scvf, faceVars, currentScvfBoundaryTypes, lateralFaceBoundaryTypes, localSubFaceIdx); | |
| 343 | 367330 | }(); | |
| 344 | |||
| 345 | 367330 | return problem.beaversJosephVelocity(element, | |
| 346 | 367330 | fvGeometry.scv(scvf.insideScvIdx()), | |
| 347 | scvf, | ||
| 348 | lateralScvf, /*on boundary*/ | ||
| 349 | innerParallelVelocity, | ||
| 350 | 367330 | tangentialVelocityGradient); | |
| 351 | } | ||
| 352 | |||
| 353 | private: | ||
| 354 | |||
| 355 | /*! | ||
| 356 | * \brief Get the location of the lateral staggered face's center. | ||
| 357 | * Only needed for boundary conditions if the current scvf or the lateral one is on a boundary. | ||
| 358 | * | ||
| 359 | * \verbatim | ||
| 360 | * --------#######o || frontal face of staggered half-control-volume | ||
| 361 | * | || | current scvf # lateral staggered face of interest (may lie on a boundary) | ||
| 362 | * | || | x dof position | ||
| 363 | * | || x~~~~> vel.Self -- element boundaries, current scvf may lie on a boundary | ||
| 364 | * | || | o position at which the boundary conditions will be evaluated | ||
| 365 | * | || | (lateralStaggeredFaceCenter) | ||
| 366 | * ---------------- | ||
| 367 | * \endverbatim | ||
| 368 | */ | ||
| 369 | 8663412 | static const GlobalPosition& lateralStaggeredFaceCenter_(const SubControlVolumeFace& scvf, const int localSubFaceIdx) | |
| 370 | { | ||
| 371 | 8663412 | return scvf.pairData(localSubFaceIdx).lateralStaggeredFaceCenter; | |
| 372 | }; | ||
| 373 | }; | ||
| 374 | |||
| 375 | } // end namespace Dumux | ||
| 376 | |||
| 377 | #endif | ||
| 378 |