| 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-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 Fluidmatrixinteractions | ||
| 10 | * \brief Implementation of the capillary pressure and | ||
| 11 | * relative permeability <-> saturation relations according to van Genuchten. | ||
| 12 | */ | ||
| 13 | #ifndef DUMUX_MATERIAL_FLUIDMATRIX_VAN_GENUCHTEN_HH | ||
| 14 | #define DUMUX_MATERIAL_FLUIDMATRIX_VAN_GENUCHTEN_HH | ||
| 15 | |||
| 16 | #include <cmath> | ||
| 17 | #include <algorithm> | ||
| 18 | |||
| 19 | #include <dumux/common/parameters.hh> | ||
| 20 | #include <dumux/common/spline.hh> | ||
| 21 | #include <dumux/common/optionalscalar.hh> | ||
| 22 | #include <dumux/material/fluidmatrixinteractions/2p/materiallaw.hh> | ||
| 23 | |||
| 24 | namespace Dumux::FluidMatrix { | ||
| 25 | |||
| 26 | /*! | ||
| 27 | * \ingroup Fluidmatrixinteractions | ||
| 28 | * \brief Implementation of the van Genuchten capillary pressure <-> | ||
| 29 | * saturation relation, and relative permeability. | ||
| 30 | * | ||
| 31 | * \note Capillary pressure model from van Genuchten (1980), | ||
| 32 | * relative permeability model from Mualem (1976) | ||
| 33 | */ | ||
| 34 | class VanGenuchten | ||
| 35 | { | ||
| 36 | |||
| 37 | public: | ||
| 38 | /*! | ||
| 39 | * \brief The parameter type | ||
| 40 | * \tparam Scalar The scalar type | ||
| 41 | * \note The van Genuchten laws are parameterized with four parameters: \f$\mathrm{n, m, \alpha, l}\f$. | ||
| 42 | * | ||
| 43 | * - \f$\mathrm{\alpha}\f$ shape parameter \f$\mathrm{[1/Pa]}\f$ | ||
| 44 | * - \f$\mathrm{m}\f$ shape parameter \f$\mathrm{[-]}\f$ | ||
| 45 | * - \f$\mathrm{n}\f$ shape parameter \f$\mathrm{[-]}\f$ | ||
| 46 | * - \f$\mathrm{l}\f$ pore-connectivity parameter \f$\mathrm{[-]}\f$ of Mualem's relative permeability curve | ||
| 47 | * | ||
| 48 | * \note In the original Mualem (1976) paper the pore-connectivity parameter is called "n". It's referred to as "l" in | ||
| 49 | * several later publication of van Genuchten, e.g. van Genuchten (1991), Shaap & van Genuchten (2006). | ||
| 50 | */ | ||
| 51 | template<class Scalar> | ||
| 52 | struct Params | ||
| 53 | { | ||
| 54 | 135 | Params(Scalar alpha, Scalar n, Scalar l = 0.5) | |
| 55 | 135 | : alpha_(alpha), n_(n), m_(1.0 - 1.0/n), l_(l) | |
| 56 | {} | ||
| 57 | |||
| 58 | ✗ | Scalar alpha() const { return alpha_; } | |
| 59 | void setAlpha(Scalar alpha) { alpha_ = alpha; } | ||
| 60 | |||
| 61 | ✗ | Scalar m() const { return m_; } | |
| 62 | void setM(Scalar m) { m_ = m; n_ = 1.0/(1.0 - m); } | ||
| 63 | |||
| 64 | ✗ | Scalar n() const{ return n_; } | |
| 65 | void setN(Scalar n){ n_ = n; m_ = 1.0 - 1.0/n; } | ||
| 66 | |||
| 67 | ✗ | Scalar l() const { return l_; } | |
| 68 | void setL(Scalar l) { l_ = l; } | ||
| 69 | |||
| 70 | 4527 | bool operator== (const Params& p) const | |
| 71 | { | ||
| 72 |
2/2✓ Branch 0 taken 63 times.
✓ Branch 1 taken 4464 times.
|
4527 | return Dune::FloatCmp::eq(alpha_, p.alpha_, 1e-6) |
| 73 |
2/4✗ Branch 0 not taken.
✓ Branch 1 taken 4401 times.
✓ Branch 2 taken 4401 times.
✗ Branch 3 not taken.
|
4401 | && Dune::FloatCmp::eq(n_, p.n_, 1e-6) |
| 74 |
2/4✗ Branch 0 not taken.
✓ Branch 1 taken 4401 times.
✓ Branch 2 taken 4401 times.
✗ Branch 3 not taken.
|
4401 | && Dune::FloatCmp::eq(m_, p.m_, 1e-6) |
| 75 |
4/6✓ Branch 0 taken 4401 times.
✓ Branch 1 taken 126 times.
✗ Branch 2 not taken.
✓ Branch 3 taken 4401 times.
✗ Branch 4 not taken.
✓ Branch 5 taken 4401 times.
|
8928 | && Dune::FloatCmp::eq(l_, p.l_, 1e-6); |
| 76 | } | ||
| 77 | |||
| 78 | private: | ||
| 79 | Scalar alpha_, n_, m_, l_; | ||
| 80 | }; | ||
| 81 | |||
| 82 | /*! | ||
| 83 | * \brief Construct from a subgroup from the global parameter tree | ||
| 84 | * \note This will give you nice error messages if a mandatory parameter is missing | ||
| 85 | */ | ||
| 86 | template<class Scalar = double> | ||
| 87 | 134 | static Params<Scalar> makeParams(const std::string& paramGroup) | |
| 88 | { | ||
| 89 | 134 | const auto n = getParamFromGroup<Scalar>(paramGroup, "VanGenuchtenN"); | |
| 90 | 134 | const auto alpha = getParamFromGroup<Scalar>(paramGroup, "VanGenuchtenAlpha"); | |
| 91 | // l is usually chosen to be 0.5 (according to Mualem (1976), WRR) | ||
| 92 | 134 | const auto l = getParamFromGroup<Scalar>(paramGroup, "VanGenuchtenL", 0.5); | |
| 93 | 268 | return Params<Scalar>(alpha, n, l); | |
| 94 | } | ||
| 95 | |||
| 96 | /*! | ||
| 97 | * \brief The capillary pressure-saturation curve according to van Genuchten. | ||
| 98 | * | ||
| 99 | * Van Genuchten's empirical capillary pressure <-> saturation | ||
| 100 | * function is given by | ||
| 101 | * \f$\mathrm{ | ||
| 102 | p_c = (\overline{S}_w^{-1/m} - 1)^{1/n}/\alpha | ||
| 103 | }\f$ | ||
| 104 | * \param swe Effective saturation of the wetting phase \f$\mathrm{\overline{S}_w}\f$ | ||
| 105 | * \param params A container object that is populated with the appropriate coefficients for the respective law. | ||
| 106 | * \note Instead of undefined behaviour if swe is not in the valid range, we return a valid number, | ||
| 107 | * by clamping the input. Note that pc(swe = 0.0) = inf, have a look at RegularizedVanGenuchten if this is a problem. | ||
| 108 | */ | ||
| 109 | template<class Scalar> | ||
| 110 | 13014759 | static Scalar pc(Scalar swe, const Params<Scalar>& params) | |
| 111 | { | ||
| 112 | using std::pow; | ||
| 113 | using std::clamp; | ||
| 114 | |||
| 115 |
1/2✓ Branch 0 taken 13014759 times.
✗ Branch 1 not taken.
|
13014759 | swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0 |
| 116 | |||
| 117 | 13014759 | const Scalar pc = pow(pow(swe, -1.0/params.m()) - 1, 1.0/params.n())/params.alpha(); | |
| 118 | 13014759 | return pc; | |
| 119 | } | ||
| 120 | |||
| 121 | /*! | ||
| 122 | * \brief The saturation-capillary pressure curve according to van Genuchten. | ||
| 123 | * | ||
| 124 | * This is the inverse of the capillary pressure-saturation curve: | ||
| 125 | * \f$\mathrm{ | ||
| 126 | \overline{S}_w = {p_c}^{-1} = ((\alpha p_c)^n + 1)^{-m} | ||
| 127 | }\f$ | ||
| 128 | * | ||
| 129 | * \param pc Capillary pressure \f$\mathrm{p_c}\f$ in \f$\mathrm{[Pa]}\f$ | ||
| 130 | * \param params A container object that is populated with the appropriate coefficients for the respective law. | ||
| 131 | * \return The effective saturation of the wetting phase \f$\mathrm{\overline{S}_w}\f$ | ||
| 132 | * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number, | ||
| 133 | * i.e. sw(pc < 0.0) = 0.0, by clamping the input to the physical bounds. | ||
| 134 | */ | ||
| 135 | template<class Scalar> | ||
| 136 | 793449694 | static Scalar swe(Scalar pc, const Params<Scalar>& params) | |
| 137 | { | ||
| 138 | using std::pow; | ||
| 139 | using std::max; | ||
| 140 | |||
| 141 |
1/2✗ Branch 0 not taken.
✓ Branch 1 taken 793449694 times.
|
793449694 | pc = max(pc, 0.0); // the equation below is undefined for negative pcs |
| 142 | |||
| 143 | 793449694 | const Scalar sw = pow(pow(params.alpha()*pc, params.n()) + 1, -params.m()); | |
| 144 | 793449694 | return sw; | |
| 145 | } | ||
| 146 | |||
| 147 | /*! | ||
| 148 | * \brief The capillary pressure at Swe = 1.0 also called end point capillary pressure | ||
| 149 | * \param params A container object that is populated with the appropriate coefficients for the respective law. | ||
| 150 | */ | ||
| 151 | template<class Scalar> | ||
| 152 | ✗ | static Scalar endPointPc(const Params<Scalar>& params) | |
| 153 | ✗ | { return 0.0; } | |
| 154 | |||
| 155 | /*! | ||
| 156 | * \brief The partial derivative of the capillary | ||
| 157 | * pressure w.r.t. the effective saturation according to van Genuchten. | ||
| 158 | * | ||
| 159 | * This is equivalent to | ||
| 160 | * \f$\mathrm{ | ||
| 161 | \frac{\partial p_c}{\partial \overline{S}_w} = | ||
| 162 | -\frac{1}{\alpha} (\overline{S}_w^{-1/m} - 1)^{1/n - } | ||
| 163 | \overline{S}_w^{-1/m} / \overline{S}_w / m | ||
| 164 | }\f$ | ||
| 165 | * | ||
| 166 | * \param swe Effective saturation of the wetting phase \f$\mathrm{\overline{S}_w}\f$ | ||
| 167 | * \param params A container object that is populated with the appropriate coefficients for the respective law. | ||
| 168 | * \note Instead of undefined behaviour if swe is not in the valid range, we return a valid number, | ||
| 169 | * by clamping the input. | ||
| 170 | */ | ||
| 171 | template<class Scalar> | ||
| 172 | 11658390 | static Scalar dpc_dswe(Scalar swe, const Params<Scalar>& params) | |
| 173 | { | ||
| 174 | using std::pow; | ||
| 175 | using std::clamp; | ||
| 176 | |||
| 177 |
1/2✓ Branch 0 taken 11658390 times.
✗ Branch 1 not taken.
|
11658390 | swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0 |
| 178 | |||
| 179 | 11658390 | const Scalar powSwe = pow(swe, -1/params.m()); | |
| 180 | 11658390 | return - 1.0/params.alpha() * pow(powSwe - 1, 1.0/params.n() - 1)/params.n() | |
| 181 | 11658390 | * powSwe/swe/params.m(); | |
| 182 | } | ||
| 183 | |||
| 184 | /*! | ||
| 185 | * \brief The partial derivative of the effective | ||
| 186 | * saturation to the capillary pressure according to van Genuchten. | ||
| 187 | * | ||
| 188 | * \param pc Capillary pressure \f$\mathrm{p_C}\f$ in \f$\mathrm{[Pa]}\f$ | ||
| 189 | * \param params A container object that is populated with the appropriate coefficients for the respective law. | ||
| 190 | * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number, | ||
| 191 | * by clamping the input. | ||
| 192 | */ | ||
| 193 | template<class Scalar> | ||
| 194 | 38360413 | static Scalar dswe_dpc(Scalar pc, const Params<Scalar>& params) | |
| 195 | { | ||
| 196 | using std::pow; | ||
| 197 | using std::max; | ||
| 198 | |||
| 199 |
1/2✗ Branch 0 not taken.
✓ Branch 1 taken 38360413 times.
|
38360413 | pc = max(pc, 0.0); // the equation below is undefined for negative pcs |
| 200 | |||
| 201 | 38360413 | const Scalar powAlphaPc = pow(params.alpha()*pc, params.n()); | |
| 202 | 38360413 | return -pow(powAlphaPc + 1, -params.m()-1)*params.m()*powAlphaPc/pc*params.n(); | |
| 203 | } | ||
| 204 | |||
| 205 | /*! | ||
| 206 | * \brief The relative permeability for the wetting phase of | ||
| 207 | * the medium implied by van Genuchten / Mualem | ||
| 208 | * parameterization. | ||
| 209 | * | ||
| 210 | * \param swe The mobile saturation of the wetting phase. | ||
| 211 | * \param params A container object that is populated with the appropriate coefficients for the respective law. | ||
| 212 | * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number, | ||
| 213 | * by clamping the input. | ||
| 214 | */ | ||
| 215 | template<class Scalar> | ||
| 216 | 820907417 | static Scalar krw(Scalar swe, const Params<Scalar>& params) | |
| 217 | { | ||
| 218 | using std::pow; | ||
| 219 | using std::clamp; | ||
| 220 | |||
| 221 |
1/2✓ Branch 0 taken 820907417 times.
✗ Branch 1 not taken.
|
820907417 | swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0 |
| 222 | |||
| 223 | 820907417 | const Scalar r = 1.0 - pow(1.0 - pow(swe, 1.0/params.m()), params.m()); | |
| 224 | 820907417 | return pow(swe, params.l())*r*r; | |
| 225 | } | ||
| 226 | |||
| 227 | /*! | ||
| 228 | * \brief The derivative of the relative permeability for the | ||
| 229 | * wetting phase in regard to the wetting saturation of the | ||
| 230 | * medium implied by the van Genuchten parameterization. | ||
| 231 | * | ||
| 232 | * \param swe The mobile saturation of the wetting phase. | ||
| 233 | * \param params A container object that is populated with the appropriate coefficients for the respective law. | ||
| 234 | * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number, | ||
| 235 | * by clamping the input. | ||
| 236 | */ | ||
| 237 | template<class Scalar> | ||
| 238 | 29567654 | static Scalar dkrw_dswe(Scalar swe, const Params<Scalar>& params) | |
| 239 | { | ||
| 240 | using std::pow; | ||
| 241 | using std::clamp; | ||
| 242 | |||
| 243 |
1/2✓ Branch 0 taken 29567654 times.
✗ Branch 1 not taken.
|
29567654 | swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0 |
| 244 | |||
| 245 | 29567654 | const Scalar x = 1.0 - pow(swe, 1.0/params.m()); | |
| 246 | 29567654 | const Scalar xToM = pow(x, params.m()); | |
| 247 | 29567654 | return (1.0 - xToM)*pow(swe, params.l()-1) * ( (1.0 - xToM)*params.l() + 2*xToM*(1.0-x)/x ); | |
| 248 | } | ||
| 249 | |||
| 250 | /*! | ||
| 251 | * \brief The relative permeability for the non-wetting phase | ||
| 252 | * of the medium implied by van Genuchten's | ||
| 253 | * parameterization. | ||
| 254 | * | ||
| 255 | * \param swe The mobile saturation of the wetting phase. | ||
| 256 | * \param params A container object that is populated with the appropriate coefficients for the respective law. | ||
| 257 | * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number, | ||
| 258 | * by clamping the input. | ||
| 259 | */ | ||
| 260 | template<class Scalar> | ||
| 261 | 17103047 | static Scalar krn(Scalar swe, const Params<Scalar>& params) | |
| 262 | { | ||
| 263 | using std::pow; | ||
| 264 | using std::clamp; | ||
| 265 | |||
| 266 |
1/2✓ Branch 0 taken 17103047 times.
✗ Branch 1 not taken.
|
17103047 | swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0 |
| 267 | |||
| 268 | 17103047 | return pow(1 - swe, params.l()) * pow(1 - pow(swe, 1.0/params.m()), 2*params.m()); | |
| 269 | } | ||
| 270 | |||
| 271 | /*! | ||
| 272 | * \brief The derivative of the relative permeability for the | ||
| 273 | * non-wetting phase in regard to the wetting saturation of | ||
| 274 | * the medium as implied by the van Genuchten | ||
| 275 | * parameterization. | ||
| 276 | * | ||
| 277 | * \param swe The mobile saturation of the wetting phase. | ||
| 278 | * \param params A container object that is populated with the appropriate coefficients for the respective law. | ||
| 279 | * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number, | ||
| 280 | * by clamping the input. | ||
| 281 | */ | ||
| 282 | template<class Scalar> | ||
| 283 | 1123664 | static Scalar dkrn_dswe(Scalar swe, const Params<Scalar>& params) | |
| 284 | { | ||
| 285 | using std::pow; | ||
| 286 | using std::clamp; | ||
| 287 | |||
| 288 |
1/2✓ Branch 0 taken 1123664 times.
✗ Branch 1 not taken.
|
1123664 | swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0 |
| 289 | |||
| 290 | 1123664 | const auto sne = 1.0 - swe; | |
| 291 | 1123664 | const auto x = 1.0 - pow(swe, 1.0/params.m()); | |
| 292 | 1123664 | return -pow(sne, params.l()-1.0) * pow(x, 2*params.m() - 1.0) * ( params.l()*x + 2.0*sne/swe*(1.0 - x) ); | |
| 293 | } | ||
| 294 | }; | ||
| 295 | |||
| 296 | /*! | ||
| 297 | * \ingroup Fluidmatrixinteractions | ||
| 298 | * \brief A regularization for the VanGenuchten material law | ||
| 299 | * \note Regularization can be turned of by setting the threshold parameters | ||
| 300 | * out of range (runtime) or by replacing | ||
| 301 | * this class by NoRegularization (compile time). | ||
| 302 | */ | ||
| 303 | template <class Scalar> | ||
| 304 | 480 | class VanGenuchtenRegularization | |
| 305 | { | ||
| 306 | public: | ||
| 307 | //! Regularization parameters | ||
| 308 | template<class S> | ||
| 309 | struct Params | ||
| 310 | { | ||
| 311 | /*! | ||
| 312 | * \brief Set the threshold saturation below which the capillary pressure is regularized. | ||
| 313 | * | ||
| 314 | * Most problems are very sensitive to this value (e.g. making it smaller might | ||
| 315 | * result in very high capillary pressures) | ||
| 316 | */ | ||
| 317 | ✗ | void setPcLowSwe(Scalar pcLowSwe) | |
| 318 | ✗ | { pcLowSwe_ = pcLowSwe; } | |
| 319 | |||
| 320 | /*! | ||
| 321 | * \brief Threshold saturation below which the capillary pressure is regularized. | ||
| 322 | */ | ||
| 323 | ✗ | Scalar pcLowSwe() const | |
| 324 | ✗ | { return pcLowSwe_; } | |
| 325 | |||
| 326 | /*! | ||
| 327 | * \brief Set the threshold saturation above which the capillary pressure is regularized. | ||
| 328 | */ | ||
| 329 | ✗ | void setPcHighSwe(Scalar pcHighSwe) | |
| 330 | ✗ | { pcHighSwe_ = pcHighSwe; } | |
| 331 | |||
| 332 | /*! | ||
| 333 | * \brief Threshold saturation above which the capillary pressure is regularized. | ||
| 334 | * | ||
| 335 | * Most problems are very sensitive to this value (e.g. making it smaller might | ||
| 336 | * result in negative capillary pressures). | ||
| 337 | */ | ||
| 338 | ✗ | Scalar pcHighSwe() const | |
| 339 | ✗ | { return pcHighSwe_; } | |
| 340 | |||
| 341 | /*! | ||
| 342 | * \brief Set the threshold saturation below which the relative | ||
| 343 | * permeability of the non-wetting phase gets regularized. | ||
| 344 | */ | ||
| 345 | ✗ | void setKrnLowSwe(Scalar krnLowSwe) | |
| 346 | ✗ | { krnLowSwe_ = krnLowSwe; } | |
| 347 | |||
| 348 | /*! | ||
| 349 | * \brief Threshold saturation below which the relative | ||
| 350 | * permeability of the non-wetting phase gets regularized. | ||
| 351 | */ | ||
| 352 | ✗ | Scalar krnLowSwe() const | |
| 353 | ✗ | { return krnLowSwe_; } | |
| 354 | |||
| 355 | /*! | ||
| 356 | * \brief Set the threshold saturation above which the relative | ||
| 357 | * permeability of the wetting phase gets regularized. | ||
| 358 | */ | ||
| 359 | ✗ | void setKrwHighSwe(Scalar krwHighSwe) | |
| 360 | ✗ | { krwHighSwe_ = krwHighSwe; } | |
| 361 | |||
| 362 | /*! | ||
| 363 | * \brief Threshold saturation above which the relative | ||
| 364 | * permeability of the wetting phase gets regularized. | ||
| 365 | */ | ||
| 366 | ✗ | Scalar krwHighSwe() const | |
| 367 | ✗ | { return krwHighSwe_; } | |
| 368 | |||
| 369 | private: | ||
| 370 | S pcLowSwe_ = 0.01; | ||
| 371 | S pcHighSwe_ = 0.99; | ||
| 372 | S krnLowSwe_ = 0.1; | ||
| 373 | S krwHighSwe_ = 0.9; | ||
| 374 | }; | ||
| 375 | |||
| 376 | //! Initialize the spline | ||
| 377 | template<class MaterialLaw> | ||
| 378 | 119 | void init(const MaterialLaw* m, const std::string& paramGroup) | |
| 379 | { | ||
| 380 | 119 | pcLowSwe_ = getParamFromGroup<Scalar>(paramGroup, "VanGenuchtenPcLowSweThreshold", 0.01); | |
| 381 | 119 | pcHighSwe_ = getParamFromGroup<Scalar>(paramGroup, "VanGenuchtenPcHighSweThreshold", 0.99); | |
| 382 | 119 | krwHighSwe_ = getParamFromGroup<Scalar>(paramGroup, "VanGenuchtenKrwHighSweThreshold", 0.9); | |
| 383 | 119 | krnLowSwe_ = getParamFromGroup<Scalar>(paramGroup, "VanGenuchtenKrnLowSweThreshold", 0.1); | |
| 384 | |||
| 385 | 119 | initPcParameters_(m, pcLowSwe_, pcHighSwe_); | |
| 386 | 119 | initKrParameters_(m, krnLowSwe_, krwHighSwe_); | |
| 387 | 119 | } | |
| 388 | |||
| 389 | template<class MaterialLaw, class BaseParams, class EffToAbsParams> | ||
| 390 | ✗ | void init(const MaterialLaw* m, const BaseParams& bp, const EffToAbsParams& etap, const Params<Scalar>& p) | |
| 391 | { | ||
| 392 | ✗ | pcLowSwe_ = p.pcLowSwe(); | |
| 393 | ✗ | pcHighSwe_ = p.pcHighSwe(); | |
| 394 | ✗ | krwHighSwe_ = p.krwHighSwe(); | |
| 395 | ✗ | krnLowSwe_ = p.krnLowSwe(); | |
| 396 | |||
| 397 | ✗ | initPcParameters_(m, pcLowSwe_, pcHighSwe_); | |
| 398 | ✗ | initKrParameters_(m, krnLowSwe_, krwHighSwe_); | |
| 399 | ✗ | } | |
| 400 | |||
| 401 | /*! | ||
| 402 | * \brief Equality comparison with another instance | ||
| 403 | */ | ||
| 404 | 4401 | bool operator== (const VanGenuchtenRegularization& o) const | |
| 405 | { | ||
| 406 |
1/2✗ Branch 0 not taken.
✓ Branch 1 taken 4401 times.
|
4401 | return Dune::FloatCmp::eq(pcLowSwe_, o.pcLowSwe_, 1e-6) |
| 407 |
2/4✗ Branch 0 not taken.
✓ Branch 1 taken 4401 times.
✓ Branch 2 taken 4401 times.
✗ Branch 3 not taken.
|
4401 | && Dune::FloatCmp::eq(pcHighSwe_, o.pcHighSwe_, 1e-6) |
| 408 |
2/4✗ Branch 0 not taken.
✓ Branch 1 taken 4401 times.
✓ Branch 2 taken 4401 times.
✗ Branch 3 not taken.
|
4401 | && Dune::FloatCmp::eq(krwHighSwe_, o.krwHighSwe_, 1e-6) |
| 409 |
3/6✓ Branch 0 taken 4401 times.
✗ Branch 1 not taken.
✗ Branch 2 not taken.
✓ Branch 3 taken 4401 times.
✗ Branch 4 not taken.
✓ Branch 5 taken 4401 times.
|
8802 | && Dune::FloatCmp::eq(krnLowSwe_, o.krnLowSwe_, 1e-6); |
| 410 | } | ||
| 411 | |||
| 412 | /*! | ||
| 413 | * \brief The regularized capillary pressure-saturation curve | ||
| 414 | * regularized part: | ||
| 415 | * - low saturation: extend the \f$\mathrm{p_c(S_w)}\f$ curve with the slope at the regularization point (i.e. no kink). | ||
| 416 | * - high saturation: connect the high regularization point with \f$\mathrm{\overline{S}_w =1}\f$ | ||
| 417 | * with a spline and continue linearly for \f$\mathrm{\overline{S}_w > 1}\f$ | ||
| 418 | */ | ||
| 419 | 35990053 | OptionalScalar<Scalar> pc(const Scalar swe) const | |
| 420 | { | ||
| 421 | // make sure that the capillary pressure observes a derivative | ||
| 422 | // != 0 for 'illegal' saturations. This is favourable for the | ||
| 423 | // newton solver (if the derivative is calculated numerically) | ||
| 424 | // in order to get the saturation moving to the right | ||
| 425 | // direction if it temporarily is in an 'illegal' range. | ||
| 426 |
2/2✓ Branch 0 taken 1001636 times.
✓ Branch 1 taken 34988417 times.
|
35990053 | if (swe <= pcLowSwe_) |
| 427 | 1001636 | return pcLowSwePcValue_ + pcDerivativeLowSw_*(swe - pcLowSwe_); | |
| 428 | |||
| 429 |
2/2✓ Branch 0 taken 18421512 times.
✓ Branch 1 taken 16566905 times.
|
34988417 | else if (swe >= 1.0) |
| 430 | 18421512 | return pcDerivativeHighSweEnd_*(swe - 1.0); | |
| 431 | |||
| 432 |
2/2✓ Branch 0 taken 6922229 times.
✓ Branch 1 taken 9644676 times.
|
16566905 | else if (swe > pcHighSwe_) |
| 433 | 6922229 | return pcSpline_.eval(swe); | |
| 434 | |||
| 435 | else | ||
| 436 | 9644676 | return {}; // no regularization | |
| 437 | } | ||
| 438 | |||
| 439 | /*! | ||
| 440 | * \brief The regularized partial derivative of the capillary pressure w.r.t. the saturation | ||
| 441 | */ | ||
| 442 | 1743816 | OptionalScalar<Scalar> dpc_dswe(const Scalar swe) const | |
| 443 | { | ||
| 444 |
2/2✓ Branch 0 taken 22 times.
✓ Branch 1 taken 1743794 times.
|
1743816 | if (swe <= pcLowSwe_) |
| 445 | 22 | return pcDerivativeLowSw_; | |
| 446 | |||
| 447 |
2/2✓ Branch 0 taken 1566190 times.
✓ Branch 1 taken 177604 times.
|
1743794 | else if (swe >= 1.0) |
| 448 | 1566190 | return pcDerivativeHighSweEnd_; | |
| 449 | |||
| 450 |
2/2✓ Branch 0 taken 85488 times.
✓ Branch 1 taken 92116 times.
|
177604 | else if (swe > pcHighSwe_) |
| 451 | 85488 | return pcSpline_.evalDerivative(swe); | |
| 452 | |||
| 453 | else | ||
| 454 | 92116 | return {}; // no regularization | |
| 455 | } | ||
| 456 | |||
| 457 | /*! | ||
| 458 | * \brief The regularized saturation-capillary pressure curve | ||
| 459 | */ | ||
| 460 | 810745599 | OptionalScalar<Scalar> swe(const Scalar pc) const | |
| 461 | { | ||
| 462 |
2/2✓ Branch 0 taken 19760766 times.
✓ Branch 1 taken 790984833 times.
|
810745599 | if (pc <= 0.0) |
| 463 | { | ||
| 464 |
2/2✓ Branch 0 taken 19120175 times.
✓ Branch 1 taken 640591 times.
|
19760766 | if (pcHighSwe_ >= 1.0) |
| 465 | 19120175 | return 1.0; | |
| 466 | else | ||
| 467 | 640591 | return pc/pcDerivativeHighSweEnd_ + 1.0; | |
| 468 | } | ||
| 469 | |||
| 470 | // invert spline | ||
| 471 |
2/2✓ Branch 0 taken 55773 times.
✓ Branch 1 taken 790929060 times.
|
790984833 | else if (pc <= pcHighSwePcValue_) |
| 472 | 55773 | return pcSpline_.intersectInterval(pcHighSwe_, 1.0, 0.0, 0.0, 0.0, pc); | |
| 473 | |||
| 474 |
2/2✓ Branch 0 taken 3441979 times.
✓ Branch 1 taken 787487081 times.
|
790929060 | else if (pc >= pcLowSwePcValue_) |
| 475 | 3441979 | return (pc - pcLowSwePcValue_)/pcDerivativeLowSw_ + pcLowSwe_; | |
| 476 | |||
| 477 | else | ||
| 478 | 787487081 | return {}; // no regularization | |
| 479 | } | ||
| 480 | |||
| 481 | /*! | ||
| 482 | * \brief The regularized partial derivative of the saturation to the capillary pressure | ||
| 483 | */ | ||
| 484 | 41607302 | OptionalScalar<Scalar> dswe_dpc(const Scalar pc) const | |
| 485 | { | ||
| 486 |
2/2✓ Branch 0 taken 3752283 times.
✓ Branch 1 taken 37855019 times.
|
41607302 | if (pc <= 0.0) |
| 487 | { | ||
| 488 |
2/2✓ Branch 0 taken 3752263 times.
✓ Branch 1 taken 20 times.
|
3752283 | if (pcHighSwe_ >= 1.0) |
| 489 | 3752263 | return 0.0; | |
| 490 | else | ||
| 491 | 20 | return 1.0/pcDerivativeHighSweEnd_; | |
| 492 | } | ||
| 493 | |||
| 494 | // derivative of the inverse of the function is one over derivative of the function | ||
| 495 |
2/2✓ Branch 0 taken 2 times.
✓ Branch 1 taken 37855017 times.
|
37855019 | else if (pc <= pcHighSwePcValue_) |
| 496 | 2 | return 1.0/pcSpline_.evalDerivative(pcSpline_.intersectInterval(pcHighSwe_, 1.0, 0.0, 0.0, 0.0, pc)); | |
| 497 | |||
| 498 |
2/2✓ Branch 0 taken 494606 times.
✓ Branch 1 taken 37360411 times.
|
37855017 | else if (pc >= pcLowSwePcValue_) |
| 499 | 494606 | return 1.0/pcDerivativeLowSw_; | |
| 500 | |||
| 501 | else | ||
| 502 | 37360411 | return {}; // no regularization | |
| 503 | } | ||
| 504 | |||
| 505 | /*! | ||
| 506 | * \brief The regularized relative permeability for the wetting phase | ||
| 507 | */ | ||
| 508 | 843935702 | OptionalScalar<Scalar> krw(const Scalar swe) const | |
| 509 | { | ||
| 510 |
2/2✓ Branch 0 taken 2917436 times.
✓ Branch 1 taken 841018266 times.
|
843935702 | if (swe <= 0.0) |
| 511 | 2917436 | return 0.0; | |
| 512 |
2/2✓ Branch 0 taken 36957808 times.
✓ Branch 1 taken 804060458 times.
|
841018266 | else if (swe >= 1.0) |
| 513 | 36957808 | return 1.0; | |
| 514 |
2/2✓ Branch 0 taken 10613293 times.
✓ Branch 1 taken 793447165 times.
|
804060458 | else if (swe >= krwHighSwe_) |
| 515 | 10613293 | return krwSpline_.eval(swe); | |
| 516 | else | ||
| 517 | 793447165 | return {}; // no regularization | |
| 518 | } | ||
| 519 | |||
| 520 | /*! | ||
| 521 | * \brief The regularized derivative of the relative permeability for the wetting phase w.r.t. saturation | ||
| 522 | */ | ||
| 523 | 34307830 | OptionalScalar<Scalar> dkrw_dswe(const Scalar swe) const | |
| 524 | { | ||
| 525 |
2/2✓ Branch 0 taken 375168 times.
✓ Branch 1 taken 33932662 times.
|
34307830 | if (swe <= 0.0) |
| 526 | 375168 | return 0.0; | |
| 527 |
2/2✓ Branch 0 taken 4057722 times.
✓ Branch 1 taken 29874940 times.
|
33932662 | else if (swe >= 1.0) |
| 528 | 4057722 | return 0.0; | |
| 529 |
2/2✓ Branch 0 taken 1307408 times.
✓ Branch 1 taken 28567532 times.
|
29874940 | else if (swe >= krwHighSwe_) |
| 530 | 1307408 | return krwSpline_.evalDerivative(swe); | |
| 531 | else | ||
| 532 | 28567532 | return {}; // no regularization | |
| 533 | } | ||
| 534 | |||
| 535 | /*! | ||
| 536 | * \brief The regularized relative permeability for the non-wetting phase | ||
| 537 | */ | ||
| 538 | 33824794 | OptionalScalar<Scalar> krn(const Scalar swe) const | |
| 539 | { | ||
| 540 |
2/2✓ Branch 0 taken 485115 times.
✓ Branch 1 taken 33339679 times.
|
33824794 | if (swe <= 0.0) |
| 541 | 485115 | return 1.0; | |
| 542 |
2/2✓ Branch 0 taken 17298757 times.
✓ Branch 1 taken 16040922 times.
|
33339679 | else if (swe >= 1.0) |
| 543 | 17298757 | return 0.0; | |
| 544 |
2/2✓ Branch 0 taken 307609 times.
✓ Branch 1 taken 15733313 times.
|
16040922 | else if (swe <= krnLowSwe_) |
| 545 | 307609 | return krnSpline_.eval(swe); | |
| 546 | else | ||
| 547 | 15733313 | return {}; // no regularization | |
| 548 | } | ||
| 549 | |||
| 550 | /*! | ||
| 551 | * \brief The regularized derivative of the relative permeability for the non-wetting phase w.r.t. saturation | ||
| 552 | */ | ||
| 553 | 1190756 | OptionalScalar<Scalar> dkrn_dswe(const Scalar swe) const | |
| 554 | { | ||
| 555 |
2/2✓ Branch 0 taken 10 times.
✓ Branch 1 taken 1190746 times.
|
1190756 | if (swe <= 0.0) |
| 556 | 10 | return 0.0; | |
| 557 |
2/2✓ Branch 0 taken 1067196 times.
✓ Branch 1 taken 123550 times.
|
1190746 | else if (swe >= 1.0) |
| 558 | 1067196 | return 0.0; | |
| 559 |
2/2✓ Branch 0 taken 8 times.
✓ Branch 1 taken 123542 times.
|
123550 | else if (swe <= krnLowSwe_) |
| 560 | 8 | return krnSpline_.evalDerivative(swe); | |
| 561 | else | ||
| 562 | 123542 | return {}; // no regularization | |
| 563 | } | ||
| 564 | |||
| 565 | private: | ||
| 566 | template<class MaterialLaw> | ||
| 567 | 120 | void initPcParameters_(const MaterialLaw* m, const Scalar lowSwe, const Scalar highSwe) | |
| 568 | { | ||
| 569 | 240 | const auto lowSw = MaterialLaw::EffToAbs::sweToSw(lowSwe, m->effToAbsParams()); | |
| 570 | 240 | const auto highSw = MaterialLaw::EffToAbs::sweToSw(highSwe, m->effToAbsParams()); | |
| 571 | 240 | const auto dsw_dswe = MaterialLaw::EffToAbs::dsw_dswe(m->effToAbsParams()); | |
| 572 | |||
| 573 | 120 | pcDerivativeLowSw_ = m->template dpc_dsw<false>(lowSw)*dsw_dswe; | |
| 574 | |||
| 575 | 120 | pcDerivativeHighSweThreshold_ = m->template dpc_dsw<false>(highSw)*dsw_dswe; | |
| 576 | 120 | pcDerivativeHighSweEnd_ = 2.0*(0.0 - m->template pc<false>(highSw))/(1.0 - highSwe); | |
| 577 | |||
| 578 | 120 | pcLowSwePcValue_ = m->template pc<false>(lowSw); | |
| 579 | 120 | pcHighSwePcValue_ = m->template pc<false>(highSw); | |
| 580 | |||
| 581 | // Only initialize regularization spline if given parameters are in | ||
| 582 | // the admissible range. When constructing with non-sensible parameters | ||
| 583 | // the spline construction might fail (e.g. highSwe == 1.0) | ||
| 584 |
2/2✓ Branch 0 taken 107 times.
✓ Branch 1 taken 13 times.
|
120 | if (highSwe < 1.0) |
| 585 | 107 | pcSpline_ = Spline<Scalar>(highSwe, 1.0, // x0, x1 | |
| 586 | pcHighSwePcValue_, 0, // y0, y1 | ||
| 587 | pcDerivativeHighSweThreshold_, pcDerivativeHighSweEnd_); // m0, m1 | ||
| 588 | 120 | } | |
| 589 | |||
| 590 | template<class MaterialLaw> | ||
| 591 | 120 | void initKrParameters_(const MaterialLaw* m, const Scalar lowSwe, const Scalar highSwe) | |
| 592 | { | ||
| 593 | 240 | const auto lowSw = MaterialLaw::EffToAbs::sweToSw(lowSwe, m->effToAbsParams()); | |
| 594 | 240 | const auto highSw = MaterialLaw::EffToAbs::sweToSw(highSwe, m->effToAbsParams()); | |
| 595 | 240 | const auto dsw_dswe = MaterialLaw::EffToAbs::dsw_dswe(m->effToAbsParams()); | |
| 596 | |||
| 597 | 120 | const auto krwHighSw = m->template krw<false>(highSw); | |
| 598 | 120 | const auto dkrwHighSw = m->template dkrw_dsw<false>(highSw)*dsw_dswe; | |
| 599 | |||
| 600 | 120 | const auto krnLowSw = m->template krn<false>(lowSw); | |
| 601 | 120 | const auto dkrnLowSw = m->template dkrn_dsw<false>(lowSw)*dsw_dswe; | |
| 602 | |||
| 603 |
2/2✓ Branch 0 taken 112 times.
✓ Branch 1 taken 8 times.
|
120 | if (highSwe < 1.0) |
| 604 | 112 | krwSpline_ = Spline<Scalar>(highSwe, 1.0, // x0, x1 | |
| 605 | krwHighSw, 1.0, // y0, y1 | ||
| 606 | dkrwHighSw, 0.0); // m0, m1 | ||
| 607 | |||
| 608 |
2/2✓ Branch 0 taken 118 times.
✓ Branch 1 taken 2 times.
|
120 | if (lowSwe > 0.0) |
| 609 | 118 | krnSpline_ = Spline<Scalar>(0.0, lowSwe, // x0, x1 | |
| 610 | 1.0, krnLowSw, // y0, y1 | ||
| 611 | 0.0, dkrnLowSw); // m0, m1 | ||
| 612 | 120 | } | |
| 613 | |||
| 614 | Scalar pcLowSwe_, pcHighSwe_; | ||
| 615 | Scalar pcLowSwePcValue_, pcHighSwePcValue_; | ||
| 616 | Scalar krwHighSwe_, krnLowSwe_; | ||
| 617 | Scalar pcDerivativeLowSw_; | ||
| 618 | Scalar pcDerivativeHighSweThreshold_, pcDerivativeHighSweEnd_; | ||
| 619 | |||
| 620 | Spline<Scalar> pcSpline_; | ||
| 621 | Spline<Scalar> krwSpline_; | ||
| 622 | Spline<Scalar> krnSpline_; | ||
| 623 | }; | ||
| 624 | |||
| 625 | /*! | ||
| 626 | * \ingroup Fluidmatrixinteractions | ||
| 627 | * \brief A default configuration for using the VanGenuchten material law | ||
| 628 | */ | ||
| 629 | template<typename Scalar = double> | ||
| 630 | using VanGenuchtenDefault = TwoPMaterialLaw<Scalar, VanGenuchten, VanGenuchtenRegularization<Scalar>, TwoPEffToAbsDefaultPolicy>; | ||
| 631 | |||
| 632 | /*! | ||
| 633 | * \ingroup Fluidmatrixinteractions | ||
| 634 | * \brief A default configuration without regularization for using the VanGenuchten material law | ||
| 635 | */ | ||
| 636 | template<typename Scalar = double> | ||
| 637 | using VanGenuchtenNoReg = TwoPMaterialLaw<Scalar, VanGenuchten, NoRegularization, TwoPEffToAbsDefaultPolicy>; | ||
| 638 | |||
| 639 | } // end namespace Dumux::FluidMatrix | ||
| 640 | |||
| 641 | #endif | ||
| 642 |