Instability in Leapfrog and Forward-Backward Schemes

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Title:	Instability in Leapfrog and Forward-Backward Schemes
Authors:	Sun,WY
Contributors:	大氣物理研究所
Keywords:	INTERNAL GRAVITY-WAVES
Date:	2010
Issue Date:	2012-03-27 17:29:27 (UTC+8)
Publisher:	國立中央大學
Abstract:	This paper shows that in the linearized shallow-water equations, the numerical schemes can become weakly unstable for the 2 Delta x wave in the C grid when the Courant number is 1 in the forward-backward scheme and 0.5 in the leapfrog scheme because of the repeated eigenvalues in the matrices. The instability can be amplified and spread to other waves and smaller Courant number if the diffusion term is included. However, Shuman smoothing can control the instability.
Relation:	MONTHLY WEATHER REVIEW
Appears in Collections:	[Department of Atmospheric Sciences and Graduate Institute of Atmospheric Physics ] journal & Dissertation

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