4. Non-incremental form for corrector-step

The origin point is refreshed using the winds V^* obtained after completion of the predictor step. Hence we obtain a refreshed origin point O^* through the origin-point research algorithm using this new wind. This refreshed origin point O^* replaces O for all the interpolations applied during the corrector step.

$\begin{displaymath}\frac{X^+_F - X^0_{O^*}}{\Delta t} = \frac{(1+ \epsilon){\bf ... ...\frac{(1+ \epsilon)X^*_F + (1 - \epsilon) X^0_{O^*}}{2}\right) \end{displaymath}$

$\Longrightarrow$

$\begin{displaymath}\frac{X^+_F - X^0_{O^*}}{\Delta t} = \frac{(1+ \epsilon){\bf ... ...ft(\frac{(1+ \epsilon) X^+_F - (1+ \epsilon)X^*_F}{2} \right) \end{displaymath}$

(4)

$\Longrightarrow$

$\begin{displaymath}\left[{\bf I} - (1 + \epsilon) \frac{\Delta t}{2} {\bf L}^*\r... ...frac{\Delta t}{2} \left[(1+ \epsilon) {\bf L}^*(X^*_F) \right] \end{displaymath}$

(5)

Pierre BENARD
2002-06-17

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