2. Non-incremental (classical) form for a 2TL-NE predictor-step

Traditionally, the form is non-incremental, i.e. the time discretization is applied to the state-variable X itself. Let us examine how write a 2TL-NE predictor-step with first-order SI-decentering.

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

$\Longrightarrow$

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

(1)

$\Longrightarrow$

$\begin{displaymath}\left[{\bf I} - (1 + \epsilon) \frac{\Delta t}{2} {\bf L}^*\r... ...\right] - (1 + \epsilon) \frac{\Delta t}{2} {\bf L}^*(X^0_F) \end{displaymath}$

(2)

Pierre BENARD
2002-06-17

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