GCC Code Coverage Report


Directory: ../../../builds/dumux-repositories/
File: /builds/dumux-repositories/dumux/dumux/material/fluidmatrixinteractions/2p/brookscorey.hh
Date: 2024-09-21 20:52:54
Exec Total Coverage
Lines: 87 104 83.7%
Functions: 12 22 54.5%
Branches: 58 92 63.0%

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 Brooks and Corey.
12 */
13 #ifndef DUMUX_MATERIAL_FLUIDMATRIX_BROOKS_COREY_HH
14 #define DUMUX_MATERIAL_FLUIDMATRIX_BROOKS_COREY_HH
15
16 #include <cmath>
17 #include <algorithm>
18
19 #include <dumux/common/parameters.hh>
20 #include <dumux/common/optionalscalar.hh>
21 #include <dumux/material/fluidmatrixinteractions/2p/materiallaw.hh>
22
23 namespace Dumux::FluidMatrix {
24
25 /*!
26 * \ingroup Fluidmatrixinteractions
27 *
28 * \brief Implementation of the Brooks-Corey capillary pressure <->
29 * saturation relation. This class bundles the "raw" curves
30 * as static members and doesn't concern itself converting
31 * absolute to effective saturations and vice versa.
32 *
33 * For general info: EffToAbsLaw
34 *
35 *\see BrooksCoreyParams
36 */
37 class BrooksCorey
38 {
39 public:
40 /*!
41 * \brief The parameter type
42 * \tparam Scalar The scalar type
43 * \note The Brooks Corey laws are parameterized with two parameters: \f$\mathrm{p_{ce}, \lambda}\f$,
44 * the capillary entry pressure in \f$\mathrm{[Pa]}\f$] and a dimensionless shape parameter, respectively.
45 */
46 template<class Scalar>
47 struct Params
48 {
49 7 Params(Scalar pcEntry, Scalar lambda)
50
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7 : pcEntry_(pcEntry), lambda_(lambda)
51 {}
52
53 Scalar pcEntry() const{ return pcEntry_; }
54 void setPcEntry(Scalar pcEntry){ pcEntry_ = pcEntry; }
55
56 Scalar lambda() const { return lambda_; }
57
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2 void setLambda(Scalar lambda) { lambda_ = lambda; }
58
59 29504 bool operator== (const Params& p) const
60 {
61
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29504 return Dune::FloatCmp::eq(pcEntry(), p.pcEntry(), 1e-6)
62
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29504 && Dune::FloatCmp::eq(lambda(), p.lambda(), 1e-6);
63 }
64
65 private:
66 Scalar pcEntry_, lambda_;
67 };
68
69 /*!
70 * \brief Construct from a subgroup from the global parameter tree
71 * \note This will give you nice error messages if a mandatory parameter is missing
72 */
73 template<class Scalar = double>
74 69 static Params<Scalar> makeParams(const std::string& paramGroup)
75 {
76 69 const auto pcEntry = getParamFromGroup<Scalar>(paramGroup, "BrooksCoreyPcEntry");
77 69 const auto lambda = getParamFromGroup<Scalar>(paramGroup, "BrooksCoreyLambda");
78 69 return {pcEntry, lambda};
79 }
80
81 /*!
82 * \brief The capillary pressure-saturation curve according to Brooks & Corey.
83 *
84 * The Brooks-Corey empirical capillary pressure <-> saturation
85 * function is given by
86 *
87 * \f$\mathrm{ p_c = p_{ce}\overline{S}_w^{-1/\lambda}
88 * }\f$
89 *
90 * \param swe Effective saturation of the wetting phase \f$\mathrm{[\overline{S}_w]}\f$
91 * \param params A container object that is populated with the appropriate coefficients for the respective law.
92 * Therefore, in the (problem specific) spatialParameters first, the material law is chosen,
93 and then the params container is constructed accordingly. Afterwards the values are set there, too.
94 * \return Capillary pressure calculated by Brooks & Corey constitutive relation.
95 *
96 * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number,
97 * by clamping the input.
98 */
99 template<class Scalar>
100 25110822 static Scalar pc(Scalar swe, const Params<Scalar>& params)
101 {
102 using std::pow;
103 using std::clamp;
104
105
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25110822 swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
106
107 25110822 return params.pcEntry()*pow(swe, -1.0/params.lambda());
108 }
109
110 /*!
111 * \brief The saturation-capillary pressure curve according to Brooks & Corey.
112 *
113 * This is the inverse of the capillary pressure-saturation curve:
114 * \f$\mathrm{ \overline{S}_w = (\frac{p_c}{p_{ce}})^{-\lambda}}\f$
115 *
116 * \param pc Capillary pressure \f$\mathrm{[p_c]}\f$ in \f$\mathrm{[Pa]}\f$.
117 * \param params A container object that is populated with the appropriate coefficients for the respective law.
118 * Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container
119 * is constructed accordingly. Afterwards the values are set there, too.
120 * \return Effective wetting phase saturation calculated as inverse of BrooksCorey constitutive relation.
121 *
122 * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number,
123 * by clamping the input.
124 */
125 template<class Scalar>
126 static Scalar swe(Scalar pc, const Params<Scalar>& params)
127 {
128 using std::pow;
129 using std::max;
130
131
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1335568 pc = max(pc, 0.0); // the equation below is undefined for negative pcs
132
133 1335568 return pow(pc/params.pcEntry(), -params.lambda());
134 }
135
136 /*!
137 * \brief The capillary pressure at Swe = 1.0 also called end point capillary pressure
138 *
139 * \param params A container object that is populated with the appropriate coefficients for the respective law.
140 * Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container
141 * is constructed accordingly. Afterwards the values are set there, too.
142 */
143 template<class Scalar>
144 static Scalar endPointPc(const Params<Scalar>& params)
145
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5676360 { return params.pcEntry(); }
146
147 /*!
148 * \brief The partial derivative of the capillary
149 * pressure w.r.t. the effective saturation according to Brooks & Corey.
150 *
151 * This is equivalent to
152 * \f$\mathrm{\frac{\partial p_c}{\partial \overline{S}_w} =
153 * -\frac{p_{ce}}{\lambda} \overline{S}_w^{-1/\lambda - 1}
154 * }\f$
155 *
156 * \param swe Effective saturation of the wetting phase \f$\mathrm{[\overline{S}_w]}\f$
157 * \param params A container object that is populated with the appropriate coefficients for the respective law.
158 * Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container
159 * is constructed accordingly. Afterwards the values are set there, too.
160 * \return Partial derivative of \f$\mathrm{[p_c]}\f$ w.r.t. effective saturation according to Brooks & Corey.
161 *
162 * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number,
163 * by clamping the input.
164 */
165 template<class Scalar>
166 314 static Scalar dpc_dswe(Scalar swe, const Params<Scalar>& params)
167 {
168 using std::pow;
169 using std::clamp;
170
171
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314 swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
172
173 314 return -params.pcEntry()/params.lambda() * pow(swe, -1.0/params.lambda() - 1.0);
174 }
175
176 /*!
177 * \brief The partial derivative of the effective
178 * saturation w.r.t. the capillary pressure according to Brooks & Corey.
179 *
180 * \param pc Capillary pressure \f$\mathrm{[p_c]}\f$ in \f$\mathrm{[Pa]}\f$.
181 * \param params A container object that is populated with the appropriate coefficients for the respective law.
182 * Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container
183 * is constructed accordingly. Afterwards the values are set there, too.
184 * \return Partial derivative of effective saturation w.r.t. \f$\mathrm{[p_c]}\f$ according to Brooks & Corey.
185 *
186 * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number,
187 * by clamping the input.
188 */
189 template<class Scalar>
190 158 static Scalar dswe_dpc(Scalar pc, const Params<Scalar>& params)
191 {
192 using std::pow;
193 using std::max;
194
195
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158 pc = max(pc, 0.0); // the equation below is undefined for negative pcs
196
197 158 return -params.lambda()/params.pcEntry() * pow(pc/params.pcEntry(), - params.lambda() - 1.0);
198 }
199
200 /*!
201 * \brief The relative permeability for the wetting phase of
202 * the medium implied by the Brooks-Corey
203 * parameterization.
204 *
205 * \param swe The mobile saturation of the wetting phase.
206 * \param params A container object that is populated with the appropriate coefficients for the respective law.
207 * Therefore, in the (problem specific) spatialParameters first, the material law is chosen,
208 * and then the params container is constructed accordingly. Afterwards the values are set there, too.
209 * \return Relative permeability of the wetting phase calculated as implied by Brooks & Corey.
210 *
211 * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number,
212 * by clamping the input.
213 */
214 template<class Scalar>
215 22145587 static Scalar krw(Scalar swe, const Params<Scalar>& params)
216 {
217 using std::pow;
218 using std::clamp;
219
220
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22145587 swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
221
222 22145587 return pow(swe, 2.0/params.lambda() + 3.0);
223 }
224
225 /*!
226 * \brief The derivative of the relative permeability for the
227 * wetting phase with regard to the wetting saturation of the
228 * medium implied by the Brooks-Corey parameterization.
229 *
230 * \param swe The mobile saturation of the wetting phase.
231 * \param params A container object that is populated with the appropriate coefficients for the respective law.
232 * Therefore, in the (problem specific) spatialParameters first, the material law is chosen,
233 * and then the params container is constructed accordingly. Afterwards the values are set there, too.
234 * \return Derivative of the relative permeability of the wetting phase w.r.t. effective wetting phase
235 * saturation calculated as implied by Brooks & Corey.
236 *
237 * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number,
238 * by clamping the input.
239 */
240 template<class Scalar>
241 80 static Scalar dkrw_dswe(Scalar swe, const Params<Scalar>& params)
242 {
243 using std::pow;
244 using std::clamp;
245
246
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80 swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
247
248 80 return (2.0/params.lambda() + 3.0)*pow(swe, 2.0/params.lambda() + 2.0);
249 }
250
251 /*!
252 * \brief The relative permeability for the non-wetting phase of
253 * the medium as implied by the Brooks-Corey
254 * parameterization.
255 *
256 * \param swe The mobile saturation of the wetting phase.
257 * \param params A container object that is populated with the appropriate coefficients for the respective law.
258 * Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container
259 * is constructed accordingly. Afterwards the values are set there, too.
260 * \return Relative permeability of the non-wetting phase calculated as implied by Brooks & Corey.
261 *
262 * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number,
263 * by clamping the input.
264 */
265 template<class Scalar>
266 22145587 static Scalar krn(Scalar swe, const Params<Scalar>& params)
267 {
268 using std::pow;
269 using std::clamp;
270
271
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22145587 swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
272
273 22145587 const Scalar exponent = 2.0/params.lambda() + 1.0;
274 22145587 const Scalar sne = 1.0 - swe;
275 22145587 return sne*sne*(1.0 - pow(swe, exponent));
276 }
277
278 /*!
279 * \brief The derivative of the relative permeability for the
280 * non-wetting phase in regard to the wetting saturation of
281 * the medium as implied by the Brooks-Corey
282 * parameterization.
283 *
284 * \param swe The mobile saturation of the wetting phase.
285 * \param params A container object that is populated with the appropriate coefficients for the respective law.
286 * Therefore, in the (problem specific) spatialParameters first, the material law is chosen,
287 * and then the params container is constructed accordingly. Afterwards the values are set there, too.
288 * \return Derivative of the relative permeability of the non-wetting phase w.r.t. effective wetting phase
289 * saturation calculated as implied by Brooks & Corey.
290 *
291 * \note Instead of undefined behaviour if pc is not in the valid range, we return a valid number,
292 * by clamping the input.
293 */
294 template<class Scalar>
295 80 static Scalar dkrn_dswe(Scalar swe, const Params<Scalar>& params)
296 {
297 using std::pow;
298 using std::clamp;
299
300
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80 swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
301
302 80 const auto lambdaInv = 1.0/params.lambda();
303 80 const auto swePow = pow(swe, 2*lambdaInv);
304 80 return 2.0*(swe - 1.0)*(1.0 + (0.5 + lambdaInv)*swePow - (1.5 + lambdaInv)*swePow*swe);
305 }
306 };
307
308 /*!
309 * \ingroup Fluidmatrixinteractions
310 * \brief A regularization for the BrooksCorey material law
311 * \note Regularization can be turned of by setting the threshold parameters
312 * out of range (runtime) or by replacing
313 * this class by NoRegularization (compile time).
314 */
315 template <class Scalar>
316 class BrooksCoreyRegularization
317 {
318 public:
319 //! Regularization parameters
320 template<class S>
321 struct Params
322 {
323 1 Params(S pcLowSwe = 0.01) : pcLowSwe_(pcLowSwe) {}
324
325 S pcLowSwe() const { return pcLowSwe_; }
326 1 void setPcLowSwe(S pcLowSwe) { pcLowSwe_ = pcLowSwe; }
327
328 private:
329 S pcLowSwe_ = 0.01;
330 };
331
332 template<class MaterialLaw>
333 67 void init(const MaterialLaw* m, const std::string& paramGroup)
334 {
335 67 pcLowSwe_ = getParamFromGroup<Scalar>(paramGroup, "BrooksCoreyPcLowSweThreshold", 0.01);
336 67 entryPressure_ = getParamFromGroup<Scalar>(paramGroup, "BrooksCoreyPcEntry");
337
338 67 initPcParameters_(m, pcLowSwe_);
339 67 }
340
341 template<class MaterialLaw, class BaseParams, class EffToAbsParams>
342 void init(const MaterialLaw* m, const BaseParams& bp, const EffToAbsParams& etap, const Params<Scalar>& p)
343 {
344 7 pcLowSwe_ = p.pcLowSwe();
345 7 entryPressure_ = bp.pcEntry();
346
347 7 initPcParameters_(m, pcLowSwe_);
348 }
349
350 /*!
351 * \brief Equality comparison with another instance
352 */
353 26340 bool operator== (const BrooksCoreyRegularization& o) const
354 {
355
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26340 return Dune::FloatCmp::eq(pcLowSwe_, o.pcLowSwe_, 1e-6)
356
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26340 && Dune::FloatCmp::eq(entryPressure_, o.entryPressure_, 1e-6);
357 }
358
359 /*!
360 * \brief The regularized capillary pressure-saturation curve
361 * regularized part:
362 * - low saturation: extend the \f$\mathrm{p_c(S_w)}\f$ curve with the slope at the regularization point (i.e. no kink).
363 * - high saturation: continue linearly
364 */
365 OptionalScalar<Scalar> pc(const Scalar swe) const
366 {
367 // make sure that the capillary pressure observes a derivative
368 // != 0 for 'illegal' saturations. This is favourable for the
369 // newton solver (if the derivative is calculated numerically)
370 // in order to get the saturation moving to the right
371 // direction if it temporarily is in an 'illegal' range.
372
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138179594 if (swe <= pcLowSwe_)
373 861485 return pcLowSwePcValue_ + pcDerivativeLowSw_*(swe - pcLowSwe_);
374
375
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137318109 else if (swe >= 1.0)
376 112207466 return pcDerivativeHighSwEnd_*(swe - 1.0) + entryPressure_;
377
378 else
379 return {}; // no regularization
380 }
381
382 /*!
383 * \brief The regularized partial derivative of the capillary pressure w.r.t. the saturation
384 */
385 OptionalScalar<Scalar> dpc_dswe(const Scalar swe) const
386 {
387
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200 if (swe <= pcLowSwe_)
388 22 return pcDerivativeLowSw_;
389
390
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178 else if (swe >= 1.0)
391 20 return pcDerivativeHighSwEnd_;
392
393 else
394 return {}; // no regularization
395 }
396
397 /*!
398 * \brief The regularized saturation-capillary pressure curve
399 */
400 OptionalScalar<Scalar> swe(const Scalar pc) const
401 {
402
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2189500 if (pc <= entryPressure_)
403 842696 return 1.0 + (pc - entryPressure_)/pcDerivativeHighSwEnd_;
404
405
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1346804 else if (pc >= pcLowSwePcValue_)
406 11236 return (pc - pcLowSwePcValue_)/pcDerivativeLowSw_ + pcLowSwe_;
407
408 else
409 return {}; // no regularization
410 }
411
412 /*!
413 * \brief The regularized partial derivative of the saturation to the capillary pressure
414 */
415 OptionalScalar<Scalar> dswe_dpc(const Scalar pc) const
416 {
417
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200 if (pc <= entryPressure_)
418 20 return 1.0/pcDerivativeHighSwEnd_;
419
420
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180 else if (pc >= pcLowSwePcValue_)
421 22 return 1.0/pcDerivativeLowSw_;
422
423 else
424 return {}; // no regularization
425 }
426
427 /*!
428 * \brief The regularized relative permeability for the wetting phase
429 */
430 OptionalScalar<Scalar> krw(const Scalar swe) const
431 {
432
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132594618 if (swe <= 0.0)
433 return 0.0;
434
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132163249 else if (swe >= 1.0)
435 return 1.0;
436 else
437 22145587 return {}; // no regularization
438 }
439
440 /*!
441 * \brief The regularized derivative of the relative permeability for the wetting phase w.r.t. saturation
442 */
443 OptionalScalar<Scalar> dkrw_dswe(const Scalar swe) const
444 {
445
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100 if (swe <= 0.0)
446 return 0.0;
447
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90 else if (swe >= 1.0)
448 return 0.0;
449 else
450 80 return {}; // no regularization
451 }
452
453 /*!
454 * \brief The regularized relative permeability for the non-wetting phase
455 */
456 OptionalScalar<Scalar> krn(const Scalar swe) const
457 {
458
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132594618 if (swe <= 0.0)
459 return 1.0;
460
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132163249 else if (swe >= 1.0)
461 return 0.0;
462 else
463 22145587 return {}; // no regularization
464 }
465
466 /*!
467 * \brief The regularized derivative of the relative permeability for the non-wetting phase w.r.t. saturation
468 */
469 OptionalScalar<Scalar> dkrn_dswe(const Scalar swe) const
470 {
471
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100 if (swe <= 0.0)
472 return 0.0;
473
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90 else if (swe >= 1.0)
474 return 0.0;
475 else
476 80 return {}; // no regularization
477 }
478
479 private:
480 template<class MaterialLaw>
481 78 void initPcParameters_(const MaterialLaw* m, const Scalar lowSwe)
482 {
483 156 const auto lowSw = MaterialLaw::EffToAbs::sweToSw(lowSwe, m->effToAbsParams());
484 156 const auto highSw = MaterialLaw::EffToAbs::sweToSw(1.0, m->effToAbsParams());
485 156 const auto dsw_dswe = MaterialLaw::EffToAbs::dsw_dswe(m->effToAbsParams());
486 78 pcDerivativeLowSw_ = m->template dpc_dsw<false>(lowSw)*dsw_dswe;
487 78 pcDerivativeHighSwEnd_ = m->template dpc_dsw<false>(highSw)*dsw_dswe;
488 78 pcLowSwePcValue_ = m->template pc<false>(lowSw);
489 78 }
490
491 Scalar pcLowSwe_;
492 Scalar pcLowSwePcValue_;
493 Scalar entryPressure_;
494 Scalar pcDerivativeLowSw_;
495 Scalar pcDerivativeHighSwEnd_;
496 };
497
498 /*!
499 * \ingroup Fluidmatrixinteractions
500 * \brief A default configuration for using the Brooks Corey material law
501 */
502 template<typename Scalar = double>
503 using BrooksCoreyDefault = TwoPMaterialLaw<Scalar, BrooksCorey, BrooksCoreyRegularization<Scalar>, TwoPEffToAbsDefaultPolicy>;
504
505 /*!
506 * \ingroup Fluidmatrixinteractions
507 * \brief A default configuration without regularization for using the Brooks Corey material law
508 */
509 template<typename Scalar = double>
510 using BrooksCoreyNoReg = TwoPMaterialLaw<Scalar, BrooksCorey, NoRegularization, TwoPEffToAbsDefaultPolicy>;
511
512 } // end namespace Dumux::FluidMatrix
513
514 #endif
515