| 384 |
a phase velocity estimated as |
a phase velocity estimated as |
| 385 |
$\frac{1}{2}\frac{\partial\chi}{\partial{t}}/\frac{\partial\chi}{\partial{x}}$. The |
$\frac{1}{2}\frac{\partial\chi}{\partial{t}}/\frac{\partial\chi}{\partial{x}}$. The |
| 386 |
numerical scheme is (as an example for an eastern boundary): |
numerical scheme is (as an example for an eastern boundary): |
| 387 |
\[\chi_{i,j,k}^{n+1} = \chi_{i,j,k}^{n} + \Delta{t} |
\[\chi_{i_{b},j,k}^{n+1} = \chi_{i_{b},j,k}^{n} + \Delta{t} |
| 388 |
(u^{n+1}+c)_{i_{b},j,k}\frac{\chi_{i_{b},j,k}^{n} |
(u^{n+1}+c)_{i_{b},j,k}\frac{\chi_{i_{b},j,k}^{n} |
| 389 |
- \chi_{i_{b}-1,j,k}^{n}}{\Delta{x}_{i_{b},j}^{C}}\mbox{, if }u_{i_{b},j,k}^{n+1}>0, |
- \chi_{i_{b}-1,j,k}^{n}}{\Delta{x}_{i_{b},j}^{C}}\mbox{, if }u_{i_{b},j,k}^{n+1}>0, |
| 390 |
\] where $i_{b}$ is the boundary index. |
\] where $i_{b}$ is the boundary index. |
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