RichardsSeff1BWsmall Class Reference

"Broadbridge-White" form of effective saturation for Kn small as a function of porepressure (not capillary pressure, so Seff = 1 for p>=0). More...

#include <RichardsSeff1BWsmall.h>

Inheritance diagram for RichardsSeff1BWsmall:

Public Member Functions
	RichardsSeff1BWsmall (const InputParameters &parameters)
Real	LambertW (const double z) const
	LambertW function, returned value satisfies W(z)*exp(W(z))=z. More...
Real	seff (std::vector< const VariableValue * > p, unsigned int qp) const
	effective saturation as a function of porepressure More...
void	dseff (std::vector< const VariableValue * > p, unsigned int qp, std::vector< Real > &result) const
	derivative of effective saturation as a function of porepressure More...
void	d2seff (std::vector< const VariableValue * > p, unsigned int qp, std::vector< std::vector< Real >> &result) const
	second derivative of effective saturation as a function of porepressure More...
void	initialize ()
void	execute ()
void	finalize ()

Protected Attributes
Real	_sn
	BW's initial effective saturation. More...
Real	_ss
	Effective saturation where porepressure = 0. More...
Real	_c
	BW's C parameter. More...
Real	_las
	BW's lambda_s parameter multiplied by (fluiddensity*gravity) More...

Detailed Description

"Broadbridge-White" form of effective saturation for Kn small as a function of porepressure (not capillary pressure, so Seff = 1 for p>=0).

See P Broadbridge and I White `‘Constant rate rainfall infiltration: A versatile nonlinear model 1. Analytic Solution’', Water Resources Research 24 (1988) 145-154

Definition at line 26 of file RichardsSeff1BWsmall.h.

Constructor & Destructor Documentation

RichardsSeff1BWsmall()

RichardsSeff1BWsmall::RichardsSeff1BWsmall

(

const InputParameters &

parameters

)

Definition at line 53 of file RichardsSeff1BWsmall.C.

  : RichardsSeff(parameters),
    _sn(getParam<Real>("Sn")),
    _ss(getParam<Real>("Ss")),
    _c(getParam<Real>("C")),
    _las(getParam<Real>("las"))
{
  if (_ss <= _sn)
    mooseError("In BW effective saturation Sn set to ",
               _sn,
               " and Ss set to ",
               _ss,
               " but these must obey Ss > Sn");
}

Member Function Documentation

d2seff()

void RichardsSeff1BWsmall::d2seff ( std::vector< const VariableValue * >  p, unsigned int  qp, std::vector< std::vector< Real >> &  result  ) const

virtual

second derivative of effective saturation as a function of porepressure

Parameters

p	porepressure in the element. Note that (*p[0])[qp] is the porepressure at quadpoint qp
qp	the quad point to evaluate effective saturation at
result	the derivtives will be placed in this array

Implements RichardsSeff.

Definition at line 176 of file RichardsSeff1BWsmall.C.

{
  result[0][0] = 0.0;
 
  Real pp = (*p[0])[qp];
  if (pp >= 0)
    return;
 
  Real x = (_c - 1) * std::exp(_c - 1 - _c * pp / _las);
  Real lamw = LambertW(x);
  result[0][0] = -Utility::pow<3>(_c) / Utility::pow<2>(_las) * lamw * (1.0 - 2.0 * lamw) /
                 Utility::pow<5>(1 + lamw);
}

dseff()

void RichardsSeff1BWsmall::dseff ( std::vector< const VariableValue * >  p, unsigned int  qp, std::vector< Real > &  result  ) const

virtual

derivative of effective saturation as a function of porepressure

Parameters

p	porepressure in the element. Note that (*p[0])[qp] is the porepressure at quadpoint qp
qp	the quad point to evaluate effective saturation at
result	the derivtives will be placed in this array

Implements RichardsSeff.

Definition at line 160 of file RichardsSeff1BWsmall.C.

{
  result[0] = 0.0;
 
  Real pp = (*p[0])[qp];
  if (pp >= 0)
    return;
 
  Real x = (_c - 1) * std::exp(_c - 1.0 - _c * pp / _las);
  Real lamw = LambertW(x);
  result[0] = Utility::pow<2>(_c) / _las * lamw / Utility::pow<3>(1 + lamw);
}

execute()

void RichardsSeff::execute ( )

inherited

Definition at line 32 of file RichardsSeff.C.

{
}

finalize()

void RichardsSeff::finalize ( )

inherited

Definition at line 37 of file RichardsSeff.C.

{
}

initialize()

void RichardsSeff::initialize ( )

inherited

Definition at line 27 of file RichardsSeff.C.

{
}

LambertW()

Real RichardsSeff1BWsmall::LambertW

(

const double

z

)

const

LambertW function, returned value satisfies W(z)*exp(W(z))=z.

Parameters

z	the z value in above expression

Definition at line 69 of file RichardsSeff1BWsmall.C.

{
  /* Lambert W function.
     Was ~/C/LambertW.c written K M Briggs Keith dot Briggs at bt dot com 97 May 21.
     Revised KMB 97 Nov 20; 98 Feb 11, Nov 24, Dec 28; 99 Jan 13; 00 Feb 23; 01 Apr 09
 
     Computes Lambert W function, principal branch.
     See LambertW1.c for -1 branch.
 
     Returned value W(z) satisfies W(z)*exp(W(z))=z
     test data...
        W(1)= 0.5671432904097838730
        W(2)= 0.8526055020137254914
        W(20)=2.2050032780240599705
     To solve (a+b*R)*exp(-c*R)-d=0 for R, use
     R=-(b*W(-exp(-a*c/b)/b*d*c)+a*c)/b/c
 
     Test:
       gcc -DTESTW LambertW.c -o LambertW -lm && LambertW
     Library:
       gcc -O3 -c LambertW.c
 
     Modified trially by Andy to use MOOSE things
  */
  mooseAssert(z > 0, "LambertW function in RichardsSeff1BWsmall called with negative argument");
 
  int i;
  const Real eps = 4.0e-16; //, em1=0.3678794411714423215955237701614608;
  Real p, e, t, w;
 
  /* Uncomment this stuff is you ever need to call with a negative argument
  if (z < -em1)
    mooseError("LambertW: bad argument ", z, "\n");
 
  if (0.0 == z)
    return 0.0;
  if (z < -em1+1e-4)
  {
    // series near -em1 in sqrt(q)
    Real q=z+em1,r=std::sqrt(q),q2=q*q,q3=q2*q;
    return
     -1.0
     +2.331643981597124203363536062168*r
     -1.812187885639363490240191647568*q
     +1.936631114492359755363277457668*r*q
     -2.353551201881614516821543561516*q2
     +3.066858901050631912893148922704*r*q2
     -4.175335600258177138854984177460*q3
     +5.858023729874774148815053846119*r*q3
      -8.401032217523977370984161688514*q3*q;  // error approx 1e-16
  }
  */
  /* initial approx for iteration... */
  if (z < 1.0)
  {
    /* series near 0 */
    p = std::sqrt(2.0 * (2.7182818284590452353602874713526625 * z + 1.0));
    w = -1.0 + p * (1.0 + p * (-0.333333333333333333333 + p * 0.152777777777777777777777));
  }
  else
    w = std::log(z); /* asymptotic */
  if (z > 3.0)
    w -= std::log(w); /* useful? */
  for (i = 0; i < 10; i++)
  {
    /* Halley iteration */
    e = std::exp(w);
    t = w * e - z;
    p = w + 1.0;
    t /= e * p - 0.5 * (p + 1.0) * t / p;
    w -= t;
    if (std::abs(t) < eps * (1.0 + std::abs(w)))
      return w; /* rel-abs error */
  }
  /* should never get here */
  mooseError("LambertW: No convergence at z= ", z, "\n");
}

Referenced by d2seff(), dseff(), and seff().

seff()

Real RichardsSeff1BWsmall::seff ( std::vector< const VariableValue * >  p, unsigned int  qp  ) const

virtual

effective saturation as a function of porepressure

Parameters

p	porepressure in the element. Note that (*p[0])[qp] is the porepressure at quadpoint qp
qp	the quad point to evaluate effective saturation at

Implements RichardsSeff.

Definition at line 148 of file RichardsSeff1BWsmall.C.

{
  Real pp = (*p[0])[qp];
  if (pp >= 0)
    return 1.0;
 
  Real x = (_c - 1.0) * std::exp(_c - 1 - _c * pp / _las);
  Real th = _c / (1.0 + LambertW(x)); // use branch 0 for positive x
  return _sn + (_ss - _sn) * th;
}

Member Data Documentation

_c

Real RichardsSeff1BWsmall::_c

protected

BW's C parameter.

Definition at line 74 of file RichardsSeff1BWsmall.h.

Referenced by d2seff(), dseff(), and seff().

_las

Real RichardsSeff1BWsmall::_las

protected

BW's lambda_s parameter multiplied by (fluiddensity*gravity)

Definition at line 77 of file RichardsSeff1BWsmall.h.

Referenced by d2seff(), dseff(), and seff().

_sn

Real RichardsSeff1BWsmall::_sn

protected

BW's initial effective saturation.

Definition at line 68 of file RichardsSeff1BWsmall.h.

Referenced by RichardsSeff1BWsmall(), and seff().

_ss

Real RichardsSeff1BWsmall::_ss

protected

Effective saturation where porepressure = 0.

Definition at line 71 of file RichardsSeff1BWsmall.h.

Referenced by RichardsSeff1BWsmall(), and seff().

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The documentation for this class was generated from the following files:

• richards/include/userobjects/RichardsSeff1BWsmall.h
• richards/src/userobjects/RichardsSeff1BWsmall.C