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Local time stepping for a mass‐consistent and time‐split advection scheme
Author(s) -
Baldauf Michael
Publication year - 2019
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.3434
Subject(s) - advection , time stepping , grid , scheme (mathematics) , domain decomposition methods , computer science , work (physics) , mathematics , decomposition , massively parallel , reproducibility , algorithm , parallel computing , mathematical analysis , physics , geometry , finite element method , statistics , discretization , thermodynamics , ecology , biology
An advection scheme that is locally mass‐conserving, positive‐definite, and has strongly reduced splitting errors in deformational flows is presented in a recent work by Bott. Additionally, a row‐oriented substepping is proposed to deal with Courant numbers C larger than one. However, this leads to either a nonlocal communication pattern or a violation of numerical reproducibility under domain decomposition in a (massively) parallel computing environment. Instead, a local time stepping is proposed here, which acts only on those grid points where C exceeds one. It is shown that this local time stepping maintains the above‐mentioned properties of the Bott scheme and that it achieves numerical reproducibility, together with a slight improvement in efficiency.