An anelastic allspeed projection method for gravitationally stratified flows

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. del 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 orography. 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.