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A split semi‐implict reformulation of the Bushby‐Timpson 10‐level model
Author(s) -
Burridge D. M.
Publication year - 1975
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.49710143006
Subject(s) - scheme (mathematics) , mathematics , grid , space (punctuation) , mathematical analysis , computer science , geometry , operating system
A split semi‐implicit reformulation of the Bushby‐Timpson 10–level model is described. The integration cycle is split into two main parts. Firstly, the dependent variables are advected by the wind using the explicit two‐step Lax‐Wendroff integration scheme with the grid staggered in time and space. Secondly, these advected values are adjusted to account for the terms that govern the motion of small amplitude inertio‐gravity waves in the model, using a combination of an unconditionally stable implicit scheme and a conditionally stable explicit scheme. A novel feature of the scheme is the implicit treatment of only two of the model's ten gravity wave modes. This split semi‐implicit scheme is more than four times as efficient as the original explicit scheme designed by Bushby and Timpson. The results of one semi‐implicit integration to 36 hours are described and compared with an integration made with Bushby and Timpson's original explicit scheme.