Stability of Semi-Implicit and Iterative Centred-Implicit Time Discretisations for various Equation Systems Used in NWP
Bénard, P.
Année de publication
2003
The stability of the classical semi-implicit scheme and some more <br>advanced iterative schemes recently proposed for NWP purposes is <br>examined. In all of these schemes, the solution of the centered-implicit<br> nonlinear equation is approached by an iterative fixed-point algorithm,<br> preconditioned by a simple, constant in time, linear operator. A <br>general methodology for assessing analytically the stability of these <br>schemes on canonical problems for a vertically unbounded atmosphere is <br>presented. The proposed method is valid for all the equation systems <br>usually employed in NWP. However, as in earlier studies, the method can <br>be applied only in simplified meteorological contexts, thus <br>overestimating the actual stability that would occur in more realistic <br>meteorological contexts. The analysis is performed in the spatially <br>continuous framework, hence allowing the elimination of the spatial <br>discretization or the boundary conditions as possible causes of the <br>fundamental instabilities linked to the time scheme itself. The general <br>method is then shown concretely to apply to various time-discretization <br>schemes and equation systems (namely, shallow-water and fully <br>compressible Euler equations). Analytical results found in the <br>literature are obtained from the proposed method, and some original <br>results are presented.</div>
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