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RichardsSUPGstandard Class Reference

standard SUPG relationships valid for the Richards equation. More...

#include <RichardsSUPGstandard.h>

Inheritance diagram for RichardsSUPGstandard:
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Public Member Functions

 RichardsSUPGstandard (const InputParameters &parameters)
 
RealVectorValue velSUPG (RealTensorValue perm, RealVectorValue gradp, Real density, RealVectorValue gravity) const
 SUPG velocity = -perm*(gradp - density*gravity) This points in direction of information propagation. More...
 
RealTensorValue dvelSUPG_dgradp (RealTensorValue perm) const
 derivative of SUPG velocity wrt gradient of porepressure More...
 
RealVectorValue dvelSUPG_dp (RealTensorValue perm, Real density_prime, RealVectorValue gravity) const
 derivative of SUPG velocity wrt porepressure (keeping gradp fixed) More...
 
RealVectorValue bb (RealVectorValue vel, int dimen, RealVectorValue xi_prime, RealVectorValue eta_prime, RealVectorValue zeta_prime) const
 |bb| ~ 2*velocity/element_length More...
 
RealVectorValue dbb2_dgradp (RealVectorValue vel, RealTensorValue dvel_dgradp, RealVectorValue xi_prime, RealVectorValue eta_prime, RealVectorValue zeta_prime) const
 derivative of bb*bb wrt gradient of porepressure More...
 
Real dbb2_dp (RealVectorValue vel, RealVectorValue dvel_dp, RealVectorValue xi_prime, RealVectorValue eta_prime, RealVectorValue zeta_prime) const
 derivative of bb*bb wrt porepressure More...
 
Real tauSUPG (RealVectorValue vel, Real traceperm, RealVectorValue b) const
 The SUPG tau parameter. More...
 
RealVectorValue dtauSUPG_dgradp (RealVectorValue vel, RealTensorValue dvel_dgradp, Real traceperm, RealVectorValue b, RealVectorValue db2_dgradp) const
 derivative of tau wrt gradient of porepressure More...
 
Real dtauSUPG_dp (RealVectorValue vel, RealVectorValue dvel_dp, Real traceperm, RealVectorValue b, Real db2_dp) const
 derivative of tau wrt porepressure (keeping gradp fixed) More...
 
bool SUPG_trivial () const
 returns false in this case since everything is trivial More...
 
void initialize ()
 
void execute ()
 
void finalize ()
 

Protected Attributes

Real _p_SUPG
 the SUPG pressure parameter This dictates how strong the SUPG is _p_SUPG large means only a little SUPG _p_SUPG small means close to fully-upwind More...
 

Private Member Functions

Real cosh_relation (Real alpha) const
 cosh(alpha)/sinh(alpha) - 1/alpha, modified at extreme values of alpha to prevent overflows More...
 
Real cosh_relation_prime (Real alpha) const
 derivative of cosh_relation wrt alpha More...
 

Detailed Description

standard SUPG relationships valid for the Richards equation.

here i use a formula for "tau" presented in Appendix A of TJR Hughes, M Mallet and A Mizukami ``A new finite element formulation for computational fluid dynamics:: II. Behond SUPG'' Computer Methods in Applied Mechanics and Engineering 54 (1986) 341–355

Definition at line 26 of file RichardsSUPGstandard.h.

Constructor & Destructor Documentation

RichardsSUPGstandard::RichardsSUPGstandard ( const InputParameters &  parameters)

Definition at line 33 of file RichardsSUPGstandard.C.

34  : RichardsSUPG(parameters), _p_SUPG(getParam<Real>("p_SUPG"))
35 {
36 }
Real _p_SUPG
the SUPG pressure parameter This dictates how strong the SUPG is _p_SUPG large means only a little SU...
RichardsSUPG(const InputParameters &parameters)
Definition: RichardsSUPG.C:21

Member Function Documentation

RealVectorValue RichardsSUPGstandard::bb ( RealVectorValue  vel,
int  dimen,
RealVectorValue  xi_prime,
RealVectorValue  eta_prime,
RealVectorValue  zeta_prime 
) const
virtual

|bb| ~ 2*velocity/element_length

Parameters
velSUPG velocity
dimendimension of problem
xi_primespatial gradient of the isoparametric coordinate xi
eta_primespatial gradient of the isoparametric coordinate eta
zeta_primespatial gradient of the isoparametric coordinate zeta

Implements RichardsSUPG.

Definition at line 83 of file RichardsSUPGstandard.C.

88 {
89  RealVectorValue b;
90  b(0) = xi_prime * vel;
91  if (dimen >= 2)
92  b(1) = eta_prime * vel;
93  if (dimen == 3)
94  b(2) = zeta_prime * vel;
95  return b;
96 }
Real RichardsSUPGstandard::cosh_relation ( Real  alpha) const
private

cosh(alpha)/sinh(alpha) - 1/alpha, modified at extreme values of alpha to prevent overflows

Definition at line 62 of file RichardsSUPGstandard.C.

Referenced by dtauSUPG_dgradp(), dtauSUPG_dp(), and tauSUPG().

63 {
64  if (alpha >= 5.0 || alpha <= -5.0)
65  return ((alpha > 0.0) ? 1.0 : -1.0) - 1.0 / alpha; // prevents overflows
66  else if (alpha == 0)
67  return 0.0;
68  return 1.0 / std::tanh(alpha) - 1.0 / alpha;
69 }
Real RichardsSUPGstandard::cosh_relation_prime ( Real  alpha) const
private

derivative of cosh_relation wrt alpha

Definition at line 72 of file RichardsSUPGstandard.C.

Referenced by dtauSUPG_dgradp(), and dtauSUPG_dp().

73 {
74  if (alpha >= 5.0 || alpha <= -5.0)
75  return 1.0 / (alpha * alpha); // prevents overflows
76  else if (alpha == 0)
77  return 1.0 / 3.0;
78  return 1.0 - Utility::pow<2>(std::cosh(alpha) / std::sinh(alpha)) + 1.0 / (alpha * alpha);
79 }
RealVectorValue RichardsSUPGstandard::dbb2_dgradp ( RealVectorValue  vel,
RealTensorValue  dvel_dgradp,
RealVectorValue  xi_prime,
RealVectorValue  eta_prime,
RealVectorValue  zeta_prime 
) const
virtual

derivative of bb*bb wrt gradient of porepressure

Parameters
velSUPG velocity
dvel_dgradpderivative of velocity wrt gradient of porepressure
xi_primespatial gradient of the isoparametric coordinate xi
eta_primespatial gradient of the isoparametric coordinate eta
zeta_primespatial gradient of the isoparametric coordinate zeta

Implements RichardsSUPG.

Definition at line 100 of file RichardsSUPGstandard.C.

105 {
106  // if dvel_dgradp is symmetric so transpose is probably a waste of time
107  return 2.0 * ((xi_prime * vel) * (dvel_dgradp.transpose() * xi_prime) +
108  (eta_prime * vel) * (dvel_dgradp.transpose() * eta_prime) +
109  (zeta_prime * vel) * (dvel_dgradp.transpose() * zeta_prime));
110 }
Real RichardsSUPGstandard::dbb2_dp ( RealVectorValue  vel,
RealVectorValue  dvel_dp,
RealVectorValue  xi_prime,
RealVectorValue  eta_prime,
RealVectorValue  zeta_prime 
) const
virtual

derivative of bb*bb wrt porepressure

Parameters
velSUPG velocity
dvel_dpderivative of velocity wrt porepressure
xi_primespatial gradient of the isoparametric coordinate xi
eta_primespatial gradient of the isoparametric coordinate eta
zeta_primespatial gradient of the isoparametric coordinate zeta

Implements RichardsSUPG.

Definition at line 114 of file RichardsSUPGstandard.C.

119 {
120  return 2.0 *
121  ((xi_prime * vel) * (dvel_dp * xi_prime) + (eta_prime * vel) * (dvel_dp * eta_prime) +
122  (zeta_prime * vel) * (dvel_dp * zeta_prime));
123 }
RealVectorValue RichardsSUPGstandard::dtauSUPG_dgradp ( RealVectorValue  vel,
RealTensorValue  dvel_dgradp,
Real  traceperm,
RealVectorValue  b,
RealVectorValue  db2_dgradp 
) const
virtual

derivative of tau wrt gradient of porepressure

Parameters
velSUPG velocity
dvel_dgradpderivative of the SUPG velocity wrt gradient of porepressure
tracepermtrace of the permeability tensor for the material
bthe b parameter: |b| ~ 2*SUPGvelocity/element_length
db2_dgradpderivative of b*b wrt gradient of porepressure

Implements RichardsSUPG.

Definition at line 146 of file RichardsSUPGstandard.C.

151 {
152  Real norm_vel = vel.norm();
153  if (norm_vel == 0)
154  return RealVectorValue();
155 
156  RealVectorValue norm_vel_dgradp(dvel_dgradp * vel / norm_vel);
157 
158  Real norm_b = b.norm();
159  if (norm_b == 0)
160  return RealVectorValue();
161  RealVectorValue norm_b_dgradp = db2_dgradp / 2.0 / norm_b;
162 
163  Real h = 2 * norm_vel / norm_b; // h is a measure of the element length in the "a" direction
164  RealVectorValue h_dgradp(2 * norm_vel_dgradp / norm_b -
165  2.0 * norm_vel * norm_b_dgradp / norm_b / norm_b);
166 
167  Real alpha = 0.5 * norm_vel * h / traceperm / _p_SUPG; // this is the Peclet number
168  RealVectorValue alpha_dgradp =
169  0.5 * (norm_vel_dgradp * h + norm_vel * h_dgradp) / traceperm / _p_SUPG;
170 
171  Real xi_tilde = RichardsSUPGstandard::cosh_relation(alpha);
172  Real xi_tilde_prime = RichardsSUPGstandard::cosh_relation_prime(alpha);
173  RealVectorValue xi_tilde_dgradp = xi_tilde_prime * alpha_dgradp;
174 
175  RealVectorValue tau_dgradp =
176  xi_tilde_dgradp / norm_b - xi_tilde * norm_b_dgradp / (norm_b * norm_b);
177 
178  return tau_dgradp;
179 }
Real _p_SUPG
the SUPG pressure parameter This dictates how strong the SUPG is _p_SUPG large means only a little SU...
Real cosh_relation_prime(Real alpha) const
derivative of cosh_relation wrt alpha
Real cosh_relation(Real alpha) const
cosh(alpha)/sinh(alpha) - 1/alpha, modified at extreme values of alpha to prevent overflows ...
Real RichardsSUPGstandard::dtauSUPG_dp ( RealVectorValue  vel,
RealVectorValue  dvel_dp,
Real  traceperm,
RealVectorValue  b,
Real  db2_dp 
) const
virtual

derivative of tau wrt porepressure (keeping gradp fixed)

Parameters
velSUPG velocity
dvel_dpderivative of the SUPG velocity wrt porepressure
tracepermtrace of the permeability tensor for the material
bthe b parameter: |b| ~ 2*SUPGvelocity/element_length
db2_dpderivative of b*b wrt porepressure

Implements RichardsSUPG.

Definition at line 182 of file RichardsSUPGstandard.C.

187 {
188  Real norm_vel = vel.norm();
189  if (norm_vel == 0.0)
190  return 0.0; // this deriv is not necessarily correct, but i can't see a better thing to do
191 
192  Real norm_vel_dp = dvel_dp * vel / norm_vel;
193 
194  Real norm_b = b.norm();
195  if (norm_b == 0)
196  return 0.0; // this deriv is not necessarily correct, but i can't see a better thing to do
197  Real norm_b_dp = db2_dp / (2.0 * norm_b);
198 
199  Real h = 2.0 * norm_vel / norm_b; // h is a measure of the element length in the "a" direction
200  Real h_dp = 2.0 * norm_vel_dp / norm_b - 2.0 * norm_vel * norm_b_dp / (norm_b * norm_b);
201 
202  Real alpha = 0.5 * norm_vel * h / (traceperm * _p_SUPG); // this is the Peclet number
203  Real alpha_dp = 0.5 * (norm_vel_dp * h + norm_vel * h_dp) / (traceperm * _p_SUPG);
204 
205  Real xi_tilde = RichardsSUPGstandard::cosh_relation(alpha);
206  Real xi_tilde_prime = RichardsSUPGstandard::cosh_relation_prime(alpha);
207  Real xi_tilde_dp = xi_tilde_prime * alpha_dp;
208 
209  // Real tau = xi_tilde/norm_b;
210  const Real tau_dp = xi_tilde_dp / norm_b - xi_tilde * norm_b_dp / (norm_b * norm_b);
211 
212  return tau_dp;
213 }
Real _p_SUPG
the SUPG pressure parameter This dictates how strong the SUPG is _p_SUPG large means only a little SU...
Real cosh_relation_prime(Real alpha) const
derivative of cosh_relation wrt alpha
Real cosh_relation(Real alpha) const
cosh(alpha)/sinh(alpha) - 1/alpha, modified at extreme values of alpha to prevent overflows ...
RealTensorValue RichardsSUPGstandard::dvelSUPG_dgradp ( RealTensorValue  perm) const
virtual

derivative of SUPG velocity wrt gradient of porepressure

Parameters
permpermeability tensor

Implements RichardsSUPG.

Definition at line 48 of file RichardsSUPGstandard.C.

49 {
50  return -perm;
51 }
RealVectorValue RichardsSUPGstandard::dvelSUPG_dp ( RealTensorValue  perm,
Real  density_prime,
RealVectorValue  gravity 
) const
virtual

derivative of SUPG velocity wrt porepressure (keeping gradp fixed)

Parameters
permpermeability tensor
density_primederivative of fluid density wrt porepressure
gravitygravitational acceleration vector

Implements RichardsSUPG.

Definition at line 54 of file RichardsSUPGstandard.C.

57 {
58  return perm * density_prime * gravity;
59 }
void RichardsSUPG::execute ( )
inherited

Definition at line 29 of file RichardsSUPG.C.

30 {
31 }
void RichardsSUPG::finalize ( )
inherited

Definition at line 34 of file RichardsSUPG.C.

35 {
36 }
void RichardsSUPG::initialize ( )
inherited

Definition at line 24 of file RichardsSUPG.C.

25 {
26 }
bool RichardsSUPGstandard::SUPG_trivial ( ) const
virtual

returns false in this case since everything is trivial

Implements RichardsSUPG.

Definition at line 216 of file RichardsSUPGstandard.C.

217 {
218  return false;
219 }
Real RichardsSUPGstandard::tauSUPG ( RealVectorValue  vel,
Real  traceperm,
RealVectorValue  b 
) const
virtual

The SUPG tau parameter.

This dictates how strong the SUPG is

Parameters
velSUPG velocity
tracepermtrace of the permeability tensor for the material
bthe b parameter: |b| ~ 2*SUPGvelocity/element_length

Implements RichardsSUPG.

Definition at line 126 of file RichardsSUPGstandard.C.

127 {
128  // vel = velocity, b = bb
129  Real norm_v = vel.norm();
130  Real norm_b = b.norm(); // Hughes et al investigate infinity-norm and 2-norm. i just use 2-norm
131  // here. norm_b ~ 2|a|/ele_length_in_direction_of_a
132 
133  if (norm_b == 0)
134  return 0.0; // Only way for norm_b=0 is for zero ele size, or vel=0. Either way we don't have
135  // to upwind.
136 
137  Real h = 2.0 * norm_v / norm_b; // h is a measure of the element length in the "a" direction
138  Real alpha = 0.5 * norm_v * h / (traceperm * _p_SUPG); // this is the Peclet number
139 
140  const Real xi_tilde = RichardsSUPGstandard::cosh_relation(alpha);
141 
142  return xi_tilde / norm_b;
143 }
Real _p_SUPG
the SUPG pressure parameter This dictates how strong the SUPG is _p_SUPG large means only a little SU...
Real cosh_relation(Real alpha) const
cosh(alpha)/sinh(alpha) - 1/alpha, modified at extreme values of alpha to prevent overflows ...
RealVectorValue RichardsSUPGstandard::velSUPG ( RealTensorValue  perm,
RealVectorValue  gradp,
Real  density,
RealVectorValue  gravity 
) const
virtual

SUPG velocity = -perm*(gradp - density*gravity) This points in direction of information propagation.

Parameters
permpermeability tensor
gradpgradient of porepressure
densityfluid density
gravitygravitational acceleration vector

Implements RichardsSUPG.

Definition at line 39 of file RichardsSUPGstandard.C.

43 {
44  return -perm * (gradp - density * gravity); // points in direction of info propagation
45 }
const std::string density
Definition: NS.h:15

Member Data Documentation

Real RichardsSUPGstandard::_p_SUPG
protected

the SUPG pressure parameter This dictates how strong the SUPG is _p_SUPG large means only a little SUPG _p_SUPG small means close to fully-upwind

Definition at line 146 of file RichardsSUPGstandard.h.

Referenced by dtauSUPG_dgradp(), dtauSUPG_dp(), and tauSUPG().


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