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
Repository Citation
Sun, Wen Yih, "Instability in Leapfrog and Forward-Backward Schemes" (2010). Department of Earth, Atmospheric, and Planetary Sciences Faculty Publications. Paper 83.
http://dx.doi.org/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