PetscLimiterLimit#

Limit the flux

Synopsis#

#include "petscfv.h" 
PetscErrorCode PetscLimiterLimit(PetscLimiter lim, PetscReal flim, PetscReal *phi)

Input Parameters#

Output Parameter#

  • phi - The limited field

Note#

Limiters given in symmetric form following Berger, Aftosmis, and Murman 2005

 The classical flux-limited formulation is psi(r) where

 r = (u[0] - u[-1]) / (u[1] - u[0])

 The second order TVD region is bounded by

 psi_minmod(r) = min(r,1)      and        psi_superbee(r) = min(2, 2r, max(1,r))

 where all limiters are implicitly clipped to be non-negative. A more convenient slope-limited form is psi(r) =
 phi(r)(r+1)/2 in which the reconstructed interface values are

 u(v) = u[0] + phi(r) (grad u)[0] v

 where v is the vector from centroid to quadrature point. In these variables, the usual limiters become

 phi_minmod(r) = 2 min(1/(1+r),r/(1+r))   phi_superbee(r) = 2 min(2/(1+r), 2r/(1+r), max(1,r)/(1+r))

 For a nicer symmetric formulation, rewrite in terms of

 f = (u[0] - u[-1]) / (u[1] - u[-1])

 where r(f) = f/(1-f). Not that r(1-f) = (1-f)/f = 1/r(f) so the symmetry condition

 phi(r) = phi(1/r)

 becomes

 w(f) = w(1-f).

 The limiters below implement this final form w(f). The reference methods are

 w_minmod(f) = 2 min(f,(1-f))             w_superbee(r) = 4 min((1-f), f)

See Also#

PetscLimiter, PetscLimiterType, PetscLimiterSetType(), PetscLimiterCreate()

Level#

beginner

Location#

src/dm/dt/fv/interface/fv.c

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