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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 FreeflowModels | ||
| 10 | * \brief This file contains different higher order methods for approximating the velocity. | ||
| 11 | */ | ||
| 12 | |||
| 13 | #ifndef DUMUX_UPWINDING_METHODS_HH | ||
| 14 | #define DUMUX_UPWINDING_METHODS_HH | ||
| 15 | |||
| 16 | #include <cmath> | ||
| 17 | #include <functional> | ||
| 18 | #include <iostream> | ||
| 19 | #include <string> | ||
| 20 | |||
| 21 | #include <dumux/common/exceptions.hh> | ||
| 22 | #include <dumux/common/parameters.hh> | ||
| 23 | |||
| 24 | namespace Dumux { | ||
| 25 | |||
| 26 | /*! | ||
| 27 | * \ingroup FreeflowModels | ||
| 28 | * \brief Available Tvd approaches | ||
| 29 | */ | ||
| 30 | enum class TvdApproach | ||
| 31 | { | ||
| 32 | none, uniform, li, hou | ||
| 33 | }; | ||
| 34 | |||
| 35 | /*! | ||
| 36 | * \ingroup FreeflowModels | ||
| 37 | * \brief Available differencing schemes | ||
| 38 | */ | ||
| 39 | enum class DifferencingScheme | ||
| 40 | { | ||
| 41 | none, vanleer, vanalbada, minmod, superbee, umist, mclimiter, wahyd | ||
| 42 | }; | ||
| 43 | |||
| 44 | /*! | ||
| 45 | * \ingroup FreeflowModels | ||
| 46 | * \brief This file contains different higher order methods for approximating the velocity. | ||
| 47 | */ | ||
| 48 | template<class Scalar, int upwindSchemeOrder> | ||
| 49 | class StaggeredUpwindMethods | ||
| 50 | { | ||
| 51 | public: | ||
| 52 | 75 | StaggeredUpwindMethods(const std::string& paramGroup = "") | |
| 53 | 75 | { | |
| 54 |
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75 | upwindWeight_ = getParamFromGroup<Scalar>(paramGroup, "Flux.UpwindWeight"); |
| 55 | |||
| 56 | if (upwindSchemeOrder > 1) | ||
| 57 | { | ||
| 58 | // Read the runtime parameters | ||
| 59 |
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2 | tvdApproach_ = tvdApproachFromString(getParamFromGroup<std::string>(paramGroup, "Flux.TvdApproach", "Uniform")); |
| 60 |
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2 | differencingScheme_ = differencingSchemeFromString(getParamFromGroup<std::string>(paramGroup, "Flux.DifferencingScheme", "Minmod")); |
| 61 | |||
| 62 | // Assign the limiter_ depending on the differencing scheme | ||
| 63 |
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2 | switch (differencingScheme_) |
| 64 | { | ||
| 65 | 2 | case DifferencingScheme::vanleer : | |
| 66 | { | ||
| 67 | 2 | limiter_ = this->vanleer; | |
| 68 | break; | ||
| 69 | } | ||
| 70 | ✗ | case DifferencingScheme::vanalbada : | |
| 71 | { | ||
| 72 | ✗ | if (tvdApproach_ == TvdApproach::hou) | |
| 73 | ✗ | DUNE_THROW(ParameterException, "\nDifferencing scheme (Van Albada) is not implemented for the Tvd approach (Hou)."); | |
| 74 | else | ||
| 75 | ✗ | limiter_ = this->vanalbada; | |
| 76 | break; | ||
| 77 | } | ||
| 78 | ✗ | case DifferencingScheme::minmod : | |
| 79 | { | ||
| 80 | ✗ | limiter_ = this->minmod; | |
| 81 | break; | ||
| 82 | } | ||
| 83 | ✗ | case DifferencingScheme::superbee : | |
| 84 | { | ||
| 85 | ✗ | limiter_ = this->superbee; | |
| 86 | break; | ||
| 87 | } | ||
| 88 | ✗ | case DifferencingScheme::umist : | |
| 89 | { | ||
| 90 | ✗ | limiter_ = this->umist; | |
| 91 | break; | ||
| 92 | } | ||
| 93 | ✗ | case DifferencingScheme::mclimiter : | |
| 94 | { | ||
| 95 | ✗ | limiter_ = this->mclimiter; | |
| 96 | break; | ||
| 97 | } | ||
| 98 | ✗ | case DifferencingScheme::wahyd : | |
| 99 | { | ||
| 100 | ✗ | limiter_ = this->wahyd; | |
| 101 | break; | ||
| 102 | } | ||
| 103 | ✗ | default: | |
| 104 | { | ||
| 105 | ✗ | DUNE_THROW(ParameterException, "\nDifferencing scheme " << static_cast<std::string>(differencingSchemeToString(differencingScheme_)) << | |
| 106 | " is not implemented.\n"); // should never be reached | ||
| 107 | break; | ||
| 108 | } | ||
| 109 | } | ||
| 110 | |||
| 111 |
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10 | if (!hasParamInGroup(paramGroup, "Flux.TvdApproach")) |
| 112 | { | ||
| 113 | ✗ | std::cout << "No TvdApproach specified. Defaulting to the Uniform method." << "\n"; | |
| 114 | std::cout << "Other available TVD approaches for uniform (and nonuniform) grids are as follows: \n" | ||
| 115 | << " " << tvdApproachToString(TvdApproach::uniform) << ": assumes a Uniform cell size distribution\n" | ||
| 116 | << " " << tvdApproachToString(TvdApproach::li) << ": Li's approach for nonuniform cell sizes\n" | ||
| 117 | ✗ | << " " << tvdApproachToString(TvdApproach::hou) << ": Hou's approach for nonuniform cell sizes \n"; | |
| 118 | ✗ | std::cout << "Each approach can be specified as written above in the Flux group under the title TvdApproach in your input file. \n"; | |
| 119 | } | ||
| 120 |
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10 | if (!hasParamInGroup(paramGroup, "Flux.DifferencingScheme")) |
| 121 | { | ||
| 122 | |||
| 123 | ✗ | std::cout << "No DifferencingScheme specified. Defaulting to the Minmod scheme." << "\n"; | |
| 124 | std::cout << "Other available Differencing Schemes are as follows: \n" | ||
| 125 | << " " << differencingSchemeToString(DifferencingScheme::vanleer) << ": The Vanleer flux limiter\n" | ||
| 126 | << " " << differencingSchemeToString(DifferencingScheme::vanalbada) << ": The Vanalbada flux limiter\n" | ||
| 127 | << " " << differencingSchemeToString(DifferencingScheme::minmod) << ": The Minmod flux limiter\n" | ||
| 128 | << " " << differencingSchemeToString(DifferencingScheme::superbee) << ": The Superbee flux limiter\n" | ||
| 129 | << " " << differencingSchemeToString(DifferencingScheme::umist) << ": The Umist flux limiter\n" | ||
| 130 | << " " << differencingSchemeToString(DifferencingScheme::mclimiter) << ": The Mclimiter flux limiter\n" | ||
| 131 | ✗ | << " " << differencingSchemeToString(DifferencingScheme::wahyd) << ": The Wahyd flux limiter"; | |
| 132 | ✗ | std::cout << "Each scheme can be specified as written above in the Flux group under the variable DifferencingScheme in your input file. \n"; | |
| 133 | } | ||
| 134 | |||
| 135 | std::cout << "Using the tvdApproach \"" << tvdApproachToString(tvdApproach_) | ||
| 136 |
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6 | << "\" and the differencing Scheme \" " << differencingSchemeToString(differencingScheme_) << "\" \n"; |
| 137 | } | ||
| 138 | else | ||
| 139 | { | ||
| 140 | // If the runtime parameters are not specified we will use upwind | ||
| 141 | 73 | tvdApproach_ = TvdApproach::none; | |
| 142 | 73 | differencingScheme_ = DifferencingScheme::none; | |
| 143 | } | ||
| 144 | 75 | } | |
| 145 | |||
| 146 | /** | ||
| 147 | * \brief Convenience function to convert user input given as std::string | ||
| 148 | * to the corresponding enum class used for choosing the TVD Approach | ||
| 149 | */ | ||
| 150 | 2 | TvdApproach tvdApproachFromString(const std::string& tvd) | |
| 151 | { | ||
| 152 |
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2 | if (tvd == "Uniform") return TvdApproach::uniform; |
| 153 |
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2 | if (tvd == "Li") return TvdApproach::li; |
| 154 |
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2 | if (tvd == "Hou") return TvdApproach::hou; |
| 155 | ✗ | DUNE_THROW(ParameterException, "\nThis tvd approach : \"" << tvd << "\" is not implemented.\n" | |
| 156 | << "The available TVD approaches for uniform (and nonuniform) grids are as follows: \n" | ||
| 157 | << tvdApproachToString(TvdApproach::uniform) << ": assumes a uniform cell size distribution\n" | ||
| 158 | << tvdApproachToString(TvdApproach::li) << ": li's approach for nonuniform cell sizes\n" | ||
| 159 | << tvdApproachToString(TvdApproach::hou) << ": hou's approach for nonuniform cell sizes"); | ||
| 160 | } | ||
| 161 | |||
| 162 | /** | ||
| 163 | * \brief return the name of the TVD approach | ||
| 164 | */ | ||
| 165 | 2 | std::string tvdApproachToString(TvdApproach tvd) | |
| 166 | { | ||
| 167 |
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2 | switch (tvd) |
| 168 | { | ||
| 169 | ✗ | case TvdApproach::uniform: return "Uniform"; | |
| 170 | ✗ | case TvdApproach::li: return "Li"; | |
| 171 | 4 | case TvdApproach::hou: return "Hou"; | |
| 172 | ✗ | default: return "Invalid"; // should never be reached | |
| 173 | } | ||
| 174 | } | ||
| 175 | |||
| 176 | /** | ||
| 177 | * \brief Convenience function to convert user input given as std::string | ||
| 178 | * to the corresponding enum class used for choosing the Discretization Method | ||
| 179 | */ | ||
| 180 | 2 | DifferencingScheme differencingSchemeFromString(const std::string& differencingScheme) | |
| 181 | { | ||
| 182 |
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2 | if (differencingScheme == "Vanleer") return DifferencingScheme::vanleer; |
| 183 | ✗ | if (differencingScheme == "Vanalbada") return DifferencingScheme::vanalbada; | |
| 184 | ✗ | if (differencingScheme == "Minmod") return DifferencingScheme::minmod; | |
| 185 | ✗ | if (differencingScheme == "Superbee") return DifferencingScheme::superbee; | |
| 186 | ✗ | if (differencingScheme == "Umist") return DifferencingScheme::umist; | |
| 187 | ✗ | if (differencingScheme == "Mclimiter") return DifferencingScheme::mclimiter; | |
| 188 | ✗ | if (differencingScheme == "Wahyd") return DifferencingScheme::wahyd; | |
| 189 | ✗ | DUNE_THROW(ParameterException, "\nThis differencing scheme: \"" << differencingScheme << "\" is not implemented.\n" | |
| 190 | << "The available differencing schemes are as follows: \n" | ||
| 191 | << differencingSchemeToString(DifferencingScheme::vanleer) << ": The Vanleer flux limiter\n" | ||
| 192 | << differencingSchemeToString(DifferencingScheme::vanalbada) << ": The VanAlbada flux limiter\n" | ||
| 193 | << differencingSchemeToString(DifferencingScheme::minmod) << ": The Min-Mod flux limiter\n" | ||
| 194 | << differencingSchemeToString(DifferencingScheme::superbee) << ": The SuperBEE flux limiter\n" | ||
| 195 | << differencingSchemeToString(DifferencingScheme::umist) << ": The UMist flux limiter\n" | ||
| 196 | << differencingSchemeToString(DifferencingScheme::mclimiter) << ": The McLimiter flux limiter\n" | ||
| 197 | << differencingSchemeToString(DifferencingScheme::wahyd) << ": The Wahyd flux limiter"); | ||
| 198 | } | ||
| 199 | |||
| 200 | /** | ||
| 201 | * \brief return the name of the Discretization Method | ||
| 202 | */ | ||
| 203 | 2 | std::string differencingSchemeToString(DifferencingScheme differencingScheme) | |
| 204 | { | ||
| 205 |
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2 | switch (differencingScheme) |
| 206 | { | ||
| 207 | 4 | case DifferencingScheme::vanleer: return "Vanleer"; | |
| 208 | ✗ | case DifferencingScheme::vanalbada: return "Vanalbada"; | |
| 209 | ✗ | case DifferencingScheme::minmod: return "Minmod"; | |
| 210 | ✗ | case DifferencingScheme::superbee: return "Superbee"; | |
| 211 | ✗ | case DifferencingScheme::umist: return "Umist"; | |
| 212 | ✗ | case DifferencingScheme::mclimiter: return "Mclimiter"; | |
| 213 | ✗ | case DifferencingScheme::wahyd: return "Wahyd"; | |
| 214 | ✗ | default: return "Invalid"; // should never be reached | |
| 215 | } | ||
| 216 | } | ||
| 217 | |||
| 218 | /** | ||
| 219 | * \brief Upwind Method | ||
| 220 | */ | ||
| 221 | ✗ | Scalar upwind(const Scalar downstreamMomentum, | |
| 222 | const Scalar upstreamMomentum) const | ||
| 223 | { | ||
| 224 | 400060983 | return (upwindWeight_ * upstreamMomentum + (1.0 - upwindWeight_) * downstreamMomentum); | |
| 225 | } | ||
| 226 | |||
| 227 | /** | ||
| 228 | * \brief Tvd Scheme: Total Variation Diminishing | ||
| 229 | * | ||
| 230 | */ | ||
| 231 | 5775101 | Scalar tvd(const std::array<Scalar,3>& momenta, | |
| 232 | const std::array<Scalar,3>& distances, | ||
| 233 | const bool selfIsUpstream, | ||
| 234 | const TvdApproach tvdApproach) const | ||
| 235 | { | ||
| 236 | 5775101 | Scalar momentum = 0.0; | |
| 237 |
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5775101 | switch(tvdApproach) |
| 238 | { | ||
| 239 | ✗ | case TvdApproach::uniform : | |
| 240 | { | ||
| 241 | ✗ | momentum += tvdUniform(momenta, distances, selfIsUpstream); | |
| 242 | ✗ | break; | |
| 243 | } | ||
| 244 | ✗ | case TvdApproach::li : | |
| 245 | { | ||
| 246 | ✗ | momentum += tvdLi(momenta, distances, selfIsUpstream); | |
| 247 | ✗ | break; | |
| 248 | } | ||
| 249 | 5775101 | case TvdApproach::hou : | |
| 250 | { | ||
| 251 | 5775101 | momentum += tvdHou(momenta, distances, selfIsUpstream); | |
| 252 | 5775101 | break; | |
| 253 | } | ||
| 254 | ✗ | default: | |
| 255 | { | ||
| 256 | ✗ | DUNE_THROW(ParameterException, "\nThis Tvd Approach is not implemented.\n"); | |
| 257 | break; | ||
| 258 | } | ||
| 259 | } | ||
| 260 | 5775101 | return momentum; | |
| 261 | } | ||
| 262 | |||
| 263 | /** | ||
| 264 | * \brief Tvd Scheme: Total Variation Diminishing | ||
| 265 | * | ||
| 266 | * This function assumes the cell size distribution to be uniform. | ||
| 267 | */ | ||
| 268 | ✗ | Scalar tvdUniform(const std::array<Scalar,3>& momenta, | |
| 269 | const std::array<Scalar,3>& distances, | ||
| 270 | const bool selfIsUpstream) const | ||
| 271 | { | ||
| 272 | using std::isfinite; | ||
| 273 | ✗ | const Scalar downstreamMomentum = momenta[0]; | |
| 274 | ✗ | const Scalar upstreamMomentum = momenta[1]; | |
| 275 | ✗ | const Scalar upUpstreamMomentum = momenta[2]; | |
| 276 | ✗ | const Scalar ratio = (upstreamMomentum - upUpstreamMomentum) / (downstreamMomentum - upstreamMomentum); | |
| 277 | |||
| 278 | // If the velocity field is uniform (like at the first newton step) we get a NaN | ||
| 279 | ✗ | if(ratio > 0.0 && isfinite(ratio)) | |
| 280 | { | ||
| 281 | ✗ | const Scalar secondOrderTerm = 0.5 * limiter_(ratio, 2.0) * (downstreamMomentum - upstreamMomentum); | |
| 282 | ✗ | return (upstreamMomentum + secondOrderTerm); | |
| 283 | } | ||
| 284 | else | ||
| 285 | return upstreamMomentum; | ||
| 286 | } | ||
| 287 | |||
| 288 | /** | ||
| 289 | * \brief Tvd Scheme: Total Variation Diminishing | ||
| 290 | * | ||
| 291 | * This function manages the non uniformities of the grid according to [Li, Liao 2007]. | ||
| 292 | * It tries to reconstruct the value for the velocity at the upstream-upstream point | ||
| 293 | * if the grid was uniform. | ||
| 294 | */ | ||
| 295 | ✗ | Scalar tvdLi(const std::array<Scalar,3>& momenta, | |
| 296 | const std::array<Scalar,3>& distances, | ||
| 297 | const bool selfIsUpstream) const | ||
| 298 | { | ||
| 299 | using std::isfinite; | ||
| 300 | ✗ | const Scalar downstreamMomentum = momenta[0]; | |
| 301 | ✗ | const Scalar upstreamMomentum = momenta[1]; | |
| 302 | ✗ | const Scalar upUpstreamMomentum = momenta[2]; | |
| 303 | ✗ | const Scalar upstreamToDownstreamDistance = distances[0]; | |
| 304 | ✗ | const Scalar upUpstreamToUpstreamDistance = distances[1]; | |
| 305 | |||
| 306 | // selfIsUpstream is required to get the correct sign because upUpstreamToUpstreamDistance is always positive | ||
| 307 | ✗ | const Scalar upUpstreamGradient = (upstreamMomentum - upUpstreamMomentum) / upUpstreamToUpstreamDistance * selfIsUpstream; | |
| 308 | |||
| 309 | // Distance between the upUpstream node and the position where it should be if the grid were uniform. | ||
| 310 | ✗ | const Scalar correctionDistance = upUpstreamToUpstreamDistance - upstreamToDownstreamDistance; | |
| 311 | ✗ | const Scalar reconstrutedUpUpstreamVelocity = upUpstreamMomentum + upUpstreamGradient * correctionDistance; | |
| 312 | ✗ | const Scalar ratio = (upstreamMomentum - reconstrutedUpUpstreamVelocity) / (downstreamMomentum - upstreamMomentum); | |
| 313 | |||
| 314 | // If the velocity field is uniform (like at the first newton step) we get a NaN | ||
| 315 | ✗ | if(ratio > 0.0 && isfinite(ratio)) | |
| 316 | { | ||
| 317 | ✗ | const Scalar secondOrderTerm = 0.5 * limiter_(ratio, 2.0) * (downstreamMomentum - upstreamMomentum); | |
| 318 | ✗ | return (upstreamMomentum + secondOrderTerm); | |
| 319 | } | ||
| 320 | else | ||
| 321 | return upstreamMomentum; | ||
| 322 | } | ||
| 323 | |||
| 324 | /** | ||
| 325 | * \brief Tvd Scheme: Total Variation Diminishing | ||
| 326 | * | ||
| 327 | * This function manages the non uniformities of the grid according to [Hou, Simons, Hinkelmann 2007]. | ||
| 328 | * It should behave better then the Li's version in very stretched grids. | ||
| 329 | */ | ||
| 330 | 5775101 | Scalar tvdHou(const std::array<Scalar,3>& momenta, | |
| 331 | const std::array<Scalar,3>& distances, | ||
| 332 | const bool selfIsUpstream) const | ||
| 333 | { | ||
| 334 | using std::isfinite; | ||
| 335 |
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5775101 | const Scalar downstreamMomentum = momenta[0]; |
| 336 |
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5775101 | const Scalar upstreamMomentum = momenta[1]; |
| 337 |
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5775101 | const Scalar upUpstreamMomentum = momenta[2]; |
| 338 |
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5775101 | const Scalar upstreamToDownstreamDistance = distances[0]; |
| 339 |
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5775101 | const Scalar upUpstreamToUpstreamDistance = distances[1]; |
| 340 |
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5775101 | const Scalar downstreamStaggeredCellSize = distances[2]; |
| 341 | 11550202 | const Scalar ratio = (upstreamMomentum - upUpstreamMomentum) / (downstreamMomentum - upstreamMomentum) | |
| 342 | 5775101 | * upstreamToDownstreamDistance / upUpstreamToUpstreamDistance; | |
| 343 | |||
| 344 | // If the velocity field is uniform (like at the first newton step) we get a NaN | ||
| 345 |
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5775101 | if(ratio > 0.0 && isfinite(ratio)) |
| 346 | { | ||
| 347 | 4725886 | const Scalar upstreamStaggeredCellSize = 0.5 * (upstreamToDownstreamDistance + upUpstreamToUpstreamDistance); | |
| 348 | 4725886 | const Scalar R = (upstreamStaggeredCellSize + downstreamStaggeredCellSize) / upstreamStaggeredCellSize; | |
| 349 |
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4725886 | const Scalar secondOrderTerm = limiter_(ratio, R) / R * (downstreamMomentum - upstreamMomentum); |
| 350 | 4725886 | return (upstreamMomentum + secondOrderTerm); | |
| 351 | } | ||
| 352 | else | ||
| 353 | return upstreamMomentum; | ||
| 354 | } | ||
| 355 | |||
| 356 | /** | ||
| 357 | * \brief Van Leer flux limiter function [Van Leer 1974] | ||
| 358 | * | ||
| 359 | * With R != 2 is the modified Van Leer flux limiter function [Hou, Simons, Hinkelmann 2007] | ||
| 360 | */ | ||
| 361 | 4725886 | static Scalar vanleer(const Scalar r, const Scalar R) | |
| 362 | { | ||
| 363 | 4725886 | return R * r / (R - 1.0 + r); | |
| 364 | } | ||
| 365 | |||
| 366 | /** | ||
| 367 | * \brief Van Albada flux limiter function [Van Albada et al. 1982] | ||
| 368 | */ | ||
| 369 | ✗ | static Scalar vanalbada(const Scalar r, const Scalar R) | |
| 370 | { | ||
| 371 | ✗ | return r * (r + 1.0) / (1.0 + r * r); | |
| 372 | } | ||
| 373 | |||
| 374 | /** | ||
| 375 | * \brief MinMod flux limiter function [Roe 1985] | ||
| 376 | */ | ||
| 377 | ✗ | static Scalar minmod(const Scalar r, const Scalar R) | |
| 378 | { | ||
| 379 | using std::min; | ||
| 380 | ✗ | return min(r, 1.0); | |
| 381 | } | ||
| 382 | |||
| 383 | /** | ||
| 384 | * \brief SUPERBEE flux limiter function [Roe 1985] | ||
| 385 | * | ||
| 386 | * With R != 2 is the modified SUPERBEE flux limiter function [Hou, Simons, Hinkelmann 2007] | ||
| 387 | */ | ||
| 388 | ✗ | static Scalar superbee(const Scalar r, const Scalar R) | |
| 389 | { | ||
| 390 | using std::min; | ||
| 391 | using std::max; | ||
| 392 | ✗ | return max(min(R * r, 1.0), min(r, R)); | |
| 393 | } | ||
| 394 | |||
| 395 | /** | ||
| 396 | * \brief UMIST flux limiter function [Lien and Leschziner 1993] | ||
| 397 | */ | ||
| 398 | ✗ | static Scalar umist(const Scalar r, const Scalar R) | |
| 399 | { | ||
| 400 | using std::min; | ||
| 401 | ✗ | return min({R * r, (r * (5.0 - R) + R - 1.0) / 4.0, (r * (R - 1.0) + 5.0 - R) / 4.0, R}); | |
| 402 | } | ||
| 403 | |||
| 404 | /* | ||
| 405 | * \brief Monotonized-Central limiter [Van Leer 1977] | ||
| 406 | */ | ||
| 407 | ✗ | static Scalar mclimiter(const Scalar r, const Scalar R) | |
| 408 | { | ||
| 409 | using std::min; | ||
| 410 | ✗ | return min({R * r, (r + 1.0) / 2.0, R}); | |
| 411 | } | ||
| 412 | |||
| 413 | /** | ||
| 414 | * \brief WAHYD Scheme [Hou, Simons, Hinkelmann 2007]; | ||
| 415 | */ | ||
| 416 | ✗ | static Scalar wahyd(const Scalar r, const Scalar R) | |
| 417 | { | ||
| 418 | using std::min; | ||
| 419 | ✗ | return r > 1 ? min((r + R * r * r) / (R + r * r), R) | |
| 420 | ✗ | : vanleer(r, R); | |
| 421 | } | ||
| 422 | |||
| 423 | //! Returns the Tvd approach | ||
| 424 | const TvdApproach& tvdApproach() const | ||
| 425 | { | ||
| 426 | return tvdApproach_; | ||
| 427 | } | ||
| 428 | |||
| 429 | //! Returns the differencing scheme | ||
| 430 | const DifferencingScheme& differencingScheme() const | ||
| 431 | { | ||
| 432 | return differencingScheme_; | ||
| 433 | } | ||
| 434 | |||
| 435 | private: | ||
| 436 | TvdApproach tvdApproach_; | ||
| 437 | DifferencingScheme differencingScheme_; | ||
| 438 | Scalar upwindWeight_; | ||
| 439 | |||
| 440 | std::function<Scalar(const Scalar, const Scalar)> limiter_; | ||
| 441 | }; | ||
| 442 | |||
| 443 | } // end namespace Dumux | ||
| 444 | |||
| 445 | #endif | ||
| 446 |