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Asymptotic analyses for atmospheric flows and the construction of asymptotically adaptive numerical methods. (English) Zbl 1050.76056
From the conclusions: The “traditional” aim of scale analysis in meteorology is to obtain simplified asymptotic limit equations that are easier to solve and understand than the more comprehensive fully compressible flow equations, in the context of atmosphere flow modelling. We propose to construct new classes of “asymptotically adaptive numerical methods”, which do solve the full three-dimensionial compressible flow equations, but use the results of asymptotic scale analysis in the design of the discretizations. Such a scheme would assess a small number of nondimensional characteristic numbers “on the fly” during a computation. These characteristic numbers are chosen so as to indicate whether the current flow state is or is not within the vicinity of a singular limit regime. As a singular limit is approached, the discretizations automatically adapt, and they merge into a scheme for asymptotic limit equations when the limit is actually achieved.

MSC:
76U05 General theory of rotating fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
86A10 Meteorology and atmospheric physics
76M99 Basic methods in fluid mechanics
Keywords:
singular limit
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