LIMITER
slope limiter for controlling numerical diffusion in MUSCL-reconstruction scheme in EULERIMPL and EULEREXPL setting
Default:
LIMITER = 5
The following limiters are implemented and can be used in the
EULERIMPL and EULEREXPL setting:
-
- LIMITER = 1 -> van Leer:
\begin{align} \phi(r) = \frac{r + |r|}{1 + |r|}\end{align}
- LIMITER = 2 -> Minmod:
\begin{align} \phi(r) = \max\big(0,\min(r,1)\big)\end{align}
- LIMITER = 3 -> Superbee:
\begin{align} \phi(r) = \max\big(0,\min(2r,1),\min(r,2)\big)\end{align}
- LIMITER = 4 -> Koren:
\begin{align} \phi(r) = \max\left(0,\min\Big(2r,\frac{1}{3}\big(1+2r\big),2\Big)\right)\end{align}
- LIMITER = 5 -> Sweby:
\begin{align} \phi(r) = \max\big(0,\min(\beta \, r,1),\min(r, \beta)\big), \qquad 1 \leq \beta \leq 2\end{align}
\( \beta\) can be controlled by BETA_FOR_LIMITER (default: \( \beta = 1.9\) )
- LIMITER = 6 -> monotoniced central (MC):
\begin{align} \phi(r) = \max\left(0,\min\Big(2r,\frac{1}{2}\big(1+r\big),2\Big)\right)\end{align}
- LIMITER = 7 -> van Albada 2:
\begin{align} \phi(r) = \frac{2r}{1 + r^2}\end{align}
- LIMITER = 8 -> Barth & Jespersen:
\begin{align} \phi(r) = \frac{1}{2}(r + 1)\min\left(\min\Big(1,\frac{4r}{r+1}\Big),\min\Big(1,\frac{4}{r+1}\Big)\right)\end{align}
- LIMITER = 9 -> 1st order Upwind:
\begin{align} \phi = 0\end{align}