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<div id="version" align=right><b>petsc-3.14.5 2021-03-03</b></div>
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<A NAME="PetscLimiterLimit"><H1>PetscLimiterLimit</H1></A>
Limit the flux
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
#include "petscfv.h"
<A HREF="../Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</A> <A HREF="../FV/PetscLimiterLimit.html#PetscLimiterLimit">PetscLimiterLimit</A>(<A HREF="../FV/PetscLimiter.html#PetscLimiter">PetscLimiter</A> lim, <A HREF="../Sys/PetscReal.html#PetscReal">PetscReal</A> flim, <A HREF="../Sys/PetscReal.html#PetscReal">PetscReal</A> *phi)
</PRE>
<H3><FONT COLOR="#CC3333">Input Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>lim </B></TD><TD>- The <A HREF="../FV/PetscLimiter.html#PetscLimiter">PetscLimiter</A>
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>flim </B></TD><TD>- The input field
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Output Parameter</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>phi </B></TD><TD>- The limited field
</TD></TR></TABLE>
<P>
Note: Limiters given in symmetric form following Berger, Aftosmis, and Murman 2005
<pre>
The classical flux-limited formulation is psi(r) where
</pre>
<pre>
</pre>
<pre>
r = (u[0] - u[-1]) / (u[1] - u[0])
</pre>
<pre>
</pre>
<pre>
The second order TVD region is bounded by
</pre>
<pre>
</pre>
<pre>
psi_minmod(r) = min(r,1) and psi_superbee(r) = min(2, 2r, max(1,r))
</pre>
<pre>
</pre>
<pre>
where all limiters are implicitly clipped to be non-negative. A more convenient slope-limited form is psi(r) =
</pre>
<pre>
phi(r)(r+1)/2 in which the reconstructed interface values are
</pre>
<pre>
</pre>
<pre>
u(v) = u[0] + phi(r) (grad u)[0] v
</pre>
<pre>
</pre>
<pre>
where v is the vector from centroid to quadrature point. In these variables, the usual limiters become
</pre>
<pre>
</pre>
<pre>
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))
</pre>
<pre>
</pre>
<pre>
For a nicer symmetric formulation, rewrite in terms of
</pre>
<pre>
</pre>
<pre>
f = (u[0] - u[-1]) / (u[1] - u[-1])
</pre>
<pre>
</pre>
<pre>
where r(f) = f/(1-f). Not that r(1-f) = (1-f)/f = 1/r(f) so the symmetry condition
</pre>
<pre>
</pre>
<pre>
phi(r) = phi(1/r)
</pre>
<pre>
</pre>
<pre>
becomes
</pre>
<pre>
</pre>
<pre>
w(f) = w(1-f).
</pre>
<pre>
</pre>
<pre>
The limiters below implement this final form w(f). The reference methods are
</pre>
<pre>
</pre>
<pre>
w_minmod(f) = 2 min(f,(1-f)) w_superbee(r) = 4 min((1-f), f)
</pre>
<P>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../FV/PetscLimiterSetType.html#PetscLimiterSetType">PetscLimiterSetType</A>(), <A HREF="../FV/PetscLimiterCreate.html#PetscLimiterCreate">PetscLimiterCreate</A>()
<BR><P><B></B><H3><FONT COLOR="#CC3333">Level</FONT></H3>beginner<BR>
<H3><FONT COLOR="#CC3333">Location</FONT></H3>
</B><A HREF="../../../src/dm/dt/fv/interface/fv.c.html#PetscLimiterLimit">src/dm/dt/fv/interface/fv.c</A>
<BR><A HREF="./index.html">Index of all FV routines</A>
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