Title

Instability in Leapfrog and Forward-Backward Schemes

Abstract

This paper shows that in the linearized shallow-water equations, the numerical schemes can become weakly unstable for the 2Δx 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.

Keywords

data assimilation, shallow-water equations, instability

Date of this Version

2010

DOI

http://dx.doi.org/10.1175/2009MWR3127.1

Volume

138

Issue

5

Pages

1497-1501

Link Out to Full Text

http://journals.ametsoc.org/doi/abs/10.1175/2009MWR3127.1