1. Introduction

When an iterative implicit scheme is used and when the first iteration (predictor-step) is treated as 2TL-NE with a "SI-decentering" which is restricted to first-order, then a slight gain in efficiency can be achieved by using a so-called "incremental" form.

Notations:

: - M : Complete (explicit) model
: - L^*: Linear model (used for SI as solver or PC scheme as solver and conditioner).
: - $\epsilon$ : first-order in time "SI-decentering" parameter
: - X^* : State after predictor step
: - X⁺ : State after corrector step
: - Y^*, Y⁺ : "incremental" variables for X^*, X⁺ (see definitions below).
: - Superscripts are relative to time discretization (or time-level), while subscripts are relative to space location (F for final point, etc...). Quantities with subscripts other than F are interpolated.
: - The RHS of a given linear equation inversion is noted with tilde. Hence the linear equation inversion always writes: ${\bf B}.\Psi = \widetilde{\Psi}$ , where ${\bf B}$ is the linear operator to be inverted, and $\Psi$ is a state vector (in full or incremental form). Note that $\widetilde{\Psi}$ does never need any subscript since this is always defined on the grid.

Next: 2. Non-incremental (classical) form Up: Main page Previous: Appendix A: Incremental vs.

Pierre BENARD
2002-06-17

Home