Baroclinic stability of two-level semi-implicit numerical methods for the 3D shallow water equations (2005)

by Francisco J. Rueda, Enrique Sanmiguel-Rojas and Ben R. Hodges

Citation: Rueda, F.J., E. Sanmiguel-Rojas, and B.R. Hodges (2005), “Baroclinic stability of two-level semi-implicit numerical methods for the 3D shallow water equations,” submitted to Journal of Computational Physics, (November, 2005).

Abstract

The baroclinic stability of a family of two time-level, semi-implicit schemes for the 3D hydrostatic, Boussinesq Navier Stokes equations (i.e. the shallow water equations) is examined in a simple 2D horizontal-vertical domain. It is demonstrated that existing low-dissipation discretization methods that are stable in the inviscid limit for barotropic flows are unstable for baroclinic flows. Furthermore, it is shown that in practice, such methods are only baroclinically stable when the integrated continuity equation is discretized with a barotropically-dissipative backwards Euler scheme. A general family of two-step predictor-corrector schemes is proposed that have better theoretical characteristics than existing single-step schemes.

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©2005 Ben R. Hodges	• last updated November 11, 2005	• UT • College of Engineering • Dept of Civil Engineering • CRWR • EFM Home •