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Stability of compact upwind‐biased finite‐difference schemes forfeedback‐coupled advection equations
Author(s) -
Jocksch A.,
Adams N. A.,
Kleiser L.
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410244
Subject(s) - upwind scheme , stability (learning theory) , mathematics , finite difference , nyquist stability criterion , advection , constraint (computer aided design) , stability theory , mathematical analysis , nonlinear system , physics , computer science , discretization , geometry , parametric statistics , statistics , quantum mechanics , machine learning , thermodynamics
A fifth‐order compact upwind‐biased finite‐difference scheme has been developed which is asymptotically stable when applied to linear 2 × 2 systems. This scheme was optimised with respect to wave propagation through the boundaries. In order to achieve asymptotic stability for such systems a sufficient stability condition, based on the Nyquist criterion of linear system theory, was included in the optimisation as additional constraint. The evaluation of the stability condition was done numerically. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)