An anelastic allspeed projection method for gravitationally stratified flows

  • Authors:

  • Caroline Gatti-Bono;Phillip Colella

  • Affiliations:

  • Lawrence Berkeley National Laboratory, Berkeley, CA;Lawrence Berkeley National Laboratory, Berkeley, CA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

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 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.