Line data    Source code

       1             : //* This file is part of the MOOSE framework
       2             : //* https://mooseframework.inl.gov
       3             : //*
       4             : //* All rights reserved, see COPYRIGHT for full restrictions
       5             : //* https://github.com/idaholab/moose/blob/master/COPYRIGHT
       6             : //*
       7             : //* Licensed under LGPL 2.1, please see LICENSE for details
       8             : //* https://www.gnu.org/licenses/lgpl-2.1.html
       9             : 
      10             : #pragma once
      11             : 
      12             : #include "MooseTypes.h"
      13             : #include "MooseError.h"
      14             : #include "libmesh/utility.h"
      15             : 
      16             : /**
      17             :  * Broadbridge-White version of relative permeability,
      18             :  * and effective saturation as a function of capillary pressure.
      19             :  * Valid for Kn small.
      20             :  * P Broadbridge, I White ``Constant rate rainfall
      21             :  * infiltration: A versatile nonlinear model, 1 Analytical solution''.
      22             :  * Water Resources Research 24 (1988) 145--154.
      23             :  */
      24             : namespace PorousFlowBroadbridgeWhite
      25             : {
      26             : /**
      27             :  * Provides the Lambert W function, which satisfies
      28             :  * W(z) * exp(W(z)) = z
      29             :  * @param z z value, which must be positive
      30             :  * @return W
      31             :  */
      32             : Real LambertW(Real z);
      33             : 
      34             : /**
      35             :  * Effective saturation as a function of capillary pressure
      36             :  * If pc>=0 this will yield 1, otherwise it will yield <1
      37             :  * @param pc capillary pressure
      38             :  * @param c BW's C parameter
      39             :  * @param sn BW's S_n parameter
      40             :  * @param ss BW's S_s parameter
      41             :  * @param las BW's lambda_s parameter
      42             :  * @return effective saturation
      43             :  */
      44             : Real effectiveSaturation(Real pc, Real c, Real sn, Real ss, Real las);
      45             : 
      46             : /**
      47             :  * Derivative of effective saturation wrt capillary pressure
      48             :  * @param pc capillary pressure
      49             :  * @param c BW's C parameter
      50             :  * @param sn BW's S_n parameter
      51             :  * @param ss BW's S_s parameter
      52             :  * @param las BW's lambda_s parameter
      53             :  * @return derivative of effective saturation wrt capillary pressure
      54             :  */
      55             : Real dEffectiveSaturation(Real pc, Real c, Real sn, Real ss, Real las);
      56             : 
      57             : /**
      58             :  * Second derivative of effective saturation wrt capillary pressure
      59             :  * @param pc capillary pressure
      60             :  * @param c BW's C parameter
      61             :  * @param sn BW's S_n parameter
      62             :  * @param ss BW's S_s parameter
      63             :  * @param las BW's lambda_s parameter
      64             :  * @return second derivative of effective saturation wrt capillary pressure
      65             :  */
      66             : Real d2EffectiveSaturation(Real pc, Real c, Real sn, Real ss, Real las);
      67             : 
      68             : /**
      69             :  * Relative permeability as a function of saturation
      70             :  * @param s saturation
      71             :  * @param c BW's C parameter
      72             :  * @param sn BW's S_n parameter
      73             :  * @param ss BW's S_s parameter
      74             :  * @param kn BW's K_n parameter
      75             :  * @param ks BW's K_s parameter
      76             :  * @return relative permeability
      77             :  */
      78             : template <typename T>
      79             : T
      80     2743111 : relativePermeability(const T & s, Real c, Real sn, Real ss, Real kn, Real ks)
      81             : {
      82     2743111 :   if (MetaPhysicL::raw_value(s) <= sn)
      83           0 :     return kn;
      84             : 
      85     2743110 :   if (MetaPhysicL::raw_value(s) >= ss)
      86           0 :     return ks;
      87             : 
      88     2718138 :   const T coef = (ks - kn) * (c - 1.0);
      89     2718139 :   const T th = (s - sn) / (ss - sn);
      90     2718138 :   const T krel = kn + coef * Utility::pow<2>(th) / (c - th);
      91     2718138 :   return krel;
      92             : }
      93             : 
      94             : /**
      95             :  * Derivative of relative permeability with respect to saturation
      96             :  * @param s saturation
      97             :  * @param c BW's C parameter
      98             :  * @param sn BW's S_n parameter
      99             :  * @param ss BW's S_s parameter
     100             :  * @param kn BW's K_n parameter
     101             :  * @param ks BW's K_s parameter
     102             :  * @return derivative of relative permeability wrt saturation
     103             :  */
     104             : Real dRelativePermeability(Real s, Real c, Real sn, Real ss, Real kn, Real ks);
     105             : 
     106             : /**
     107             :  * Second derivative of relative permeability with respect to saturation
     108             :  * @param s saturation
     109             :  * @param c BW's C parameter
     110             :  * @param sn BW's S_n parameter
     111             :  * @param ss BW's S_s parameter
     112             :  * @param kn BW's K_n parameter
     113             :  * @param ks BW's K_s parameter
     114             :  * @return second derivative of relative permeability wrt saturation
     115             :  */
     116             : Real d2RelativePermeability(Real s, Real c, Real sn, Real ss, Real kn, Real ks);
     117             : }