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Next: 2.18.4 Multi-dimensional advection Up: 2.18 Non-linear advection schemes Previous: 2.18.2 Third order direct   Contents

2.18.3 Third order direct space time with flux limiting

The overshoots in the DST3 method can be controlled with a flux limiter. The limited flux is written:

$\displaystyle F = \frac{1}{2}(u+\vert u\vert)\left( \tau_{i-1} + \psi(r^+)(\tau... ...{2}(u-\vert u\vert)\left( \tau_{i-1} + \psi(r^-)(\tau_{i} - \tau_{i-1} )\right)$ (2.197)

where
$\displaystyle r^+$ $\displaystyle =$ $\displaystyle \frac{\tau_{i-1} - \tau_{i-2}}{\tau_{i} - \tau_{i-1}}$ (2.198)
$\displaystyle r^-$ $\displaystyle =$ $\displaystyle \frac{\tau_{i+1} - \tau_{i}}{\tau_{i} - \tau_{i-1}}$ (2.199)

and the limiter is the Sweby limiter:

$\displaystyle \psi(r) = \max[0, \min[\min(1,d_0+d_1r],\frac{1-c}{c}r ]]$ (2.200)

\fbox{ \begin{minipage}{4.75in} {\em S/R GAD\_DST3FL\_ADV\_X} ({\em gad\_dst3\_a... ...bf rTrans} (argument) \par $\tau$: {\bf tracer} (argument) \par \end{minipage} }


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