Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

A hybrid Galerkin atmospheric model

S.J. Thomas*, A. St-Cyr, R.D. Nair
National Center for Atmospheric Research, 1850 Table Mesa Drive, Boulder, CO 80305, USA

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The purpose of this paper is to explore a time-split hybrid Galerkin scheme for the atmospheric shallow water equations. A nonlinear variant of operator integration factor splitting is employed as the time-stepping scheme. The hyperbolic system representing slow modes is discretized using the discontinuous Galerkin method. An implicit second-order backward differentiation formula is applied to Coriolis and gravity wave terms. The implicit system is then discretized using a spectral element or continuous Galerkin method. The advantages of such an approach include improved mass and energy conservation properties. A TVD Runge-Kutta scheme is used for sub-stepping.

Keywords:  Integration factor; High-order methods; Shallow water equations

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