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An Efficient Two‐Time‐Level Semi‐Lagrangian Semi‐Implicit Integration Scheme
Author(s) -
Temperton Clive,
Staniforth Andrew
Publication year - 1987
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.49711347714
Subject(s) - barotropic fluid , eulerian path , stability (learning theory) , computer science , scheme (mathematics) , context (archaeology) , operator (biology) , lagrangian , numerical integration , mathematics , variable (mathematics) , time delay and integration , mathematical optimization , basis (linear algebra) , finite element method , algorithm , mathematical analysis , geometry , mechanics , geology , paleontology , biochemistry , chemistry , repressor , machine learning , transcription factor , computer vision , gene , physics , thermodynamics
The semi‐implicit semi‐Lagrangian integration technique enables numerical weather prediction models to be run with much longer timesteps than permitted by a semi‐implicit Eulerian scheme. the choice of timestep can then be made on the basis of accuracy rather than stability requirements. to realize the full potential of the technique, it is important to maintain second‐order accuracy in time; this has previously been achieved by applying it in the context of a three‐time‐level integration scheme. In this paper we present a two‐time‐level version of the technique which yields the same level of accuracy for half the computational effort. Unlike other efficient two‐time‐level schemes, ours does not rely on operator splitting. We apply this scheme to a variable‐resolution barotropic finite‐element regional model with a minimum gridlength of 100 km, using timesteps of up to three hours. the results are verified against a control run with uniformly high resolution, and are shown to be of similar accuracy to those of a semi‐implicit Eulerian integration with a timestep of 10 minutes.