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Next: 2.17.3 Centered fourth order Up: 2.17 Linear advection schemes Previous: 2.17.1 Centered second order   Contents

2.17.2 Third order upwind bias advection

Upwind biased third order advection offers a relatively good compromise between accuracy and smoothness. It is not a ``positive'' scheme meaning false extrema are permitted but the amplitude of such are significantly reduced over the centered second order method.

The third order upwind fluxes are discretized:

$\displaystyle F_x$ $\displaystyle =$ $\displaystyle U \overline{\tau - \frac{1}{6} \delta_{ii} \tau}^i
+ \frac{1}{2} \vert U\vert \delta_i \frac{1}{6} \delta_{ii} \tau$ (2.178)
$\displaystyle F_y$ $\displaystyle =$ $\displaystyle V \overline{\tau - \frac{1}{6} \delta_{ii} \tau}^j
+ \frac{1}{2} \vert V\vert \delta_j \frac{1}{6} \delta_{jj} \tau$ (2.179)
$\displaystyle F_r$ $\displaystyle =$ $\displaystyle W \overline{\tau - \frac{1}{6} \delta_{ii} \tau}^k
+ \frac{1}{2} \vert W\vert \delta_k \frac{1}{6} \delta_{kk} \tau$ (2.180)

At boundaries, $ \delta_{\hat{n}} \tau$ is set to zero allowing $ \delta_{nn}$ to be evaluated. We are currently examine the accuracy of this boundary condition and the effect on the solution.

\fbox{ \begin{minipage}{4.75in}
{\em S/R GAD\_U3\_ADV\_X} ({\em gad\_u3\_adv\_x....
...bf rTrans} (argument)
$\tau$: {\bf tracer} (argument)
\end{minipage} }

Copyright 2006 Massachusetts Institute of Technology Last update 2018-01-23