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# PetscLimiterLimit

Limit the flux

### Synopsis

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

### Input Parameters

 lim - The PetscLimiter flim - The input field

### 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)
```