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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 EffectiveDiffusivity | ||
| 10 | * \brief Relation for the effective diffusion coefficient after Millington and Quirk | ||
| 11 | */ | ||
| 12 | |||
| 13 | #ifndef DUMUX_MATERIAL_DIFFUSIVITY_MILLINGTON_QUIRK_HH | ||
| 14 | #define DUMUX_MATERIAL_DIFFUSIVITY_MILLINGTON_QUIRK_HH | ||
| 15 | |||
| 16 | #include <cmath> | ||
| 17 | #include <algorithm> | ||
| 18 | |||
| 19 | namespace Dumux { | ||
| 20 | |||
| 21 | /*! | ||
| 22 | * \addtogroup EffectiveDiffusivity | ||
| 23 | * \copydetails Dumux::DiffusivityMillingtonQuirk | ||
| 24 | */ | ||
| 25 | |||
| 26 | /*! | ||
| 27 | * \ingroup EffectiveDiffusivity | ||
| 28 | * \brief Relation for the effective diffusion coefficient after Millington and Quirk | ||
| 29 | * | ||
| 30 | * ### Millington Quirk | ||
| 31 | * | ||
| 32 | * For `DiffusivityMillingtonQuirk`, | ||
| 33 | * the tortuosity coefficient is estimated after Millington and Quirk (1961) \cite millington1961 | ||
| 34 | * by | ||
| 35 | * \f[ | ||
| 36 | * \tau = \frac{1}{\phi^2} \left(\phi S_\alpha\right)^{7/3}. | ||
| 37 | * \f] | ||
| 38 | * | ||
| 39 | * See also Helmig (1997) \cite helmig1997 [page 129]. | ||
| 40 | */ | ||
| 41 | template<class Scalar> | ||
| 42 | class DiffusivityMillingtonQuirk | ||
| 43 | { | ||
| 44 | public: | ||
| 45 | /*! | ||
| 46 | * \brief Returns the effective diffusion coefficient (\f$\mathrm{m^2/s}\f$) | ||
| 47 | * | ||
| 48 | * Returns the effective diffusion coefficient (\f$\mathrm{m^2/s}\f$) | ||
| 49 | * of component \f$ \kappa \f$ (index `compIdxI`) in phase \f$ \alpha \f$ computed as | ||
| 50 | * \f$ D^\kappa_{\text{eff},\alpha} = \phi S_\alpha \tau D^\kappa_\alpha \f$. | ||
| 51 | * | ||
| 52 | * \param volVars The Volume Variables | ||
| 53 | * \param phaseIdx the index of the phase | ||
| 54 | * \param compIdxI the component index i | ||
| 55 | * \param compIdxJ the component index j | ||
| 56 | */ | ||
| 57 | template<class VolumeVariables> | ||
| 58 |
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328654008 | static Scalar effectiveDiffusionCoefficient(const VolumeVariables& volVars, |
| 59 | const int phaseIdx, | ||
| 60 | const int compIdxI, | ||
| 61 | const int compIdxJ) | ||
| 62 | { | ||
| 63 | // instead of D_eff = phi S tau D = phi S 1/phi^2 (phi S)^(7/3) D | ||
| 64 | // we implement more efficiently D_eff = phi S^3 cubicroot(phi S) D | ||
| 65 | using std::cbrt; | ||
| 66 | using std::max; | ||
| 67 |
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328654008 | const Scalar diffCoeff = volVars.diffusionCoefficient(phaseIdx, compIdxI, compIdxJ); |
| 68 | 328654008 | const Scalar porosity = volVars.porosity(); | |
| 69 |
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333946002 | const Scalar sat = max<Scalar>(volVars.saturation(phaseIdx), 0.0); |
| 70 | 328654008 | return porosity * (sat*sat*sat) * cbrt(porosity * sat) * diffCoeff; | |
| 71 | } | ||
| 72 | }; | ||
| 73 | |||
| 74 | } // end namespace Dumux | ||
| 75 | |||
| 76 | #endif | ||
| 77 |