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