This paper looks at gravitationally-stratified atmospheric flows at low Mach and Froude numbers and proposes a new algorithm to solve the compressible Euler equations, in which the asymptotic limits are recovered numerically and the boundary conditions for block-structured local refinement methods are well-posed.The model is non-hydrostatic and the numerical algorithm uses a splitting to separate the fast acoustic dynamics from the slower anelastic dynamics. The acoustic waves are treated implicitly while the anelastic dynamics is treated semi-implicitly and an embedded-boundary method is used to represent mountain ranges. We present an example that verifies our asymptotic analysis and a set of results that compares very well with the classical gravity wave results presented by Durran.

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Abstract. This paper presents a conservative front-tracking method for shocks and contact discontinuities that is second-order accurate. It is based on a volume-of-fluid method that treats the moving front with concepts similar to those of an embedded-boundary method. Special care is taken in the centering of the data to ensure the right order of accuracy at the front, and a redistribution step guarantees conservation. A suite of test problems, for tracking both shocks and contact discontinuities, is presented that confirms that the method is second-order accurate.

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