| 13 |
\\ $i,j,k$ : current index relative to X,Y,R directions; |
\\ $i,j,k$ : current index relative to X,Y,R directions; |
| 14 |
\\basic operator: |
\\basic operator: |
| 15 |
\\ $\delta_i $ : $\delta_i \Phi = \Phi_{i+1/2} - \Phi_{i-1/2} $ |
\\ $\delta_i $ : $\delta_i \Phi = \Phi_{i+1/2} - \Phi_{i-1/2} $ |
| 16 |
|
\label{eq:delta_i} |
| 17 |
\\ $\overline{~}i$ : $\overline{\Phi}^i = ( \Phi_{i+1/2} + \Phi_{i-1/2} ) / 2 $ |
\\ $\overline{~}i$ : $\overline{\Phi}^i = ( \Phi_{i+1/2} + \Phi_{i-1/2} ) / 2 $ |
| 18 |
|
\label{eq:bar_i} |
| 19 |
\\ $\delta_x $ : $\delta_x \Phi = \frac{1}{\Delta x} \delta_i \Phi $ |
\\ $\delta_x $ : $\delta_x \Phi = \frac{1}{\Delta x} \delta_i \Phi $ |
| 20 |
|
\label{eq:delta_x} |
| 21 |
\\ |
\\ |
| 22 |
\\ $\overline{\nabla}$ = gradient operator : |
\\ $\overline{\nabla}$ = gradient operator : |
| 23 |
$\overline{\nabla} \Phi = \{ \delta_x \Phi , \delta_y \Phi \}$ |
$\overline{\nabla} \Phi = \{ \delta_x \Phi , \delta_y \Phi \}$ |
| 24 |
|
\label{eq:d_grad} |
| 25 |
\\ $\overline{\nabla} \cdot$ = divergence operator : |
\\ $\overline{\nabla} \cdot$ = divergence operator : |
| 26 |
$\overline{\nabla}\cdot \vec{\mathrm{f}} = |
$\overline{\nabla}\cdot \vec{\mathrm{f}} = |
| 27 |
\frac{1}{\cal A} \{ \delta_i \Delta y \mathrm{f}_x |
\frac{1}{\cal A} \{ \delta_i \Delta y \mathrm{f}_x |
| 28 |
+ \delta_j \Delta x \mathrm{f}_y \} $ |
+ \delta_j \Delta x \mathrm{f}_y \} $ |
| 29 |
|
\label{eq:d_div} |
| 30 |
\\ $\overline{\nabla}^2 $ = Laplacien operator : |
\\ $\overline{\nabla}^2 $ = Laplacien operator : |
| 31 |
$ \overline{\nabla}^2 \Phi = |
$ \overline{\nabla}^2 \Phi = |
| 32 |
\overline{\nabla}\cdot \overline{\nabla}\Phi $ |
\overline{\nabla}\cdot \overline{\nabla}\Phi $ |
| 33 |
|
\label{eq:d_lap} |
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