627 |
\tau^{n+1/3} & = & \tau^{n} |
\tau^{n+1/3} & = & \tau^{n} |
628 |
- \Delta t \left( \frac{1}{\Delta x} \delta_i F^x(\tau^{n}) |
- \Delta t \left( \frac{1}{\Delta x} \delta_i F^x(\tau^{n}) |
629 |
+ \tau^{n} \frac{1}{\Delta x} \delta_i u \right) \\ |
+ \tau^{n} \frac{1}{\Delta x} \delta_i u \right) \\ |
630 |
\tau^{n+2/3} & = & \tau^{n} |
\tau^{n+2/3} & = & \tau^{n+1/3} |
631 |
- \Delta t \left( \frac{1}{\Delta y} \delta_j F^y(\tau^{n+1/3}) |
- \Delta t \left( \frac{1}{\Delta y} \delta_j F^y(\tau^{n+1/3}) |
632 |
+ \tau^{n} \frac{1}{\Delta y} \delta_i v \right) \\ |
+ \tau^{n} \frac{1}{\Delta y} \delta_i v \right) \\ |
633 |
\tau^{n+3/3} & = & \tau^{n} |
\tau^{n+3/3} & = & \tau^{n+2/3} |
634 |
- \Delta t \left( \frac{1}{\Delta r} \delta_k F^x(\tau^{n+2/3}) |
- \Delta t \left( \frac{1}{\Delta r} \delta_k F^x(\tau^{n+2/3}) |
635 |
+ \tau^{n} \frac{1}{\Delta r} \delta_i w \right) |
+ \tau^{n} \frac{1}{\Delta r} \delta_i w \right) |
636 |
\end{eqnarray} |
\end{eqnarray} |
678 |
Advection Scheme & code & use & use Multi- & Stencil & comments \\ |
Advection Scheme & code & use & use Multi- & Stencil & comments \\ |
679 |
& & A.B. & dimension & (1 dim) & \\ |
& & A.B. & dimension & (1 dim) & \\ |
680 |
\hline \hline |
\hline \hline |
681 |
|
$1^{rst}$order upwind & 1 & No & Yes & 3 pts & linear/$\tau$, non-linear/v\\ |
682 |
|
\hline |
683 |
centered $2^{nd}$order & 2 & Yes & No & 3 pts & linear \\ |
centered $2^{nd}$order & 2 & Yes & No & 3 pts & linear \\ |
684 |
\hline |
\hline |
685 |
$3^{rd}$order upwind & 3 & Yes & No & 5 pts & linear/$\tau$\\ |
$3^{rd}$order upwind & 3 & Yes & No & 5 pts & linear/$\tau$\\ |
686 |
\hline |
\hline |
687 |
centered $4^{th}$order & 4 & Yes & No & 5 pts & linear \\ |
centered $4^{th}$order & 4 & Yes & No & 5 pts & linear \\ |
688 |
\hline \hline |
\hline \hline |
689 |
% Lax-Wendroff & 10 & No & Yes & 3 pts & linear/tracer, non-linear/flow\\ |
$2^{nd}$order DST (Lax-Wendroff) & 20 & |
690 |
% \hline |
No & Yes & 3 pts & linear/tracer, non-linear/flow\\ |
691 |
|
\hline |
692 |
$3^{rd}$order DST & 30 & No & Yes & 5 pts & linear/$\tau$, non-linear/v\\ |
$3^{rd}$order DST & 30 & No & Yes & 5 pts & linear/$\tau$, non-linear/v\\ |
693 |
\hline \hline |
\hline \hline |
694 |
$2^{nd}$order Flux Limiters & 77 & No & Yes & 5 pts & non-linear \\ |
$2^{nd}$order Flux Limiters & 77 & No & Yes & 5 pts & non-linear \\ |