Open AccessSemi‐implicit methods, nonlinear balance, and regularized equations
Author(s) -
Reich Sebastian,
Wood Nigel,
Staniforth Andrew
Publication year - 2007
Publication title -
atmospheric science letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.951
H-Index - 45
ISSN - 1530-261X
DOI - 10.1002/asl.142
Subject(s) - regularization (linguistics) , nonlinear system , discretization , mathematics , equivalence (formal languages) , permission , computer science , mathematical analysis , artificial intelligence , pure mathematics , physics , quantum mechanics , political science , law
A regularized time‐staggered discretization of the shallow‐water equations has recently been proposed. The form of the regularization operator is chosen such that linear equivalence with the semi‐implicit method can be achieved. Here, we present a further generalization of the regularization that also takes into account nonlinear balance. The performance of the improved regularization procedure is demonstrated for a simple nonlinear test problem. © Crown Copyright 2007. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd.