Using the sound-proof limit for balanced data initialization

Abstract

There is substantial theoretical evidence that the pseudo-incompressible model (Durran 1989) is a valid approximation to the equations of fully compressible flow in meso-scale atmospheric flow regimes. Arguably, numerical methods for the integration of the compressible flow equations should then produce essentially pseudoincompressible results at low flow speeds if the initial data are acoustically balanced. This paper summarizes the construction of a compressible flow solver that observes this desirable. Given a pseudo-incompressible solver, the design of the scheme requires little additional coding as it exploits the close structural similarity of the compressible and pseudo-incompressible model equations. The modified scheme allows us to solve the compressible, pseudo-incompressible, and a continuous family of intermediate models, all of which conserve a model-dependent total energy. We conjecture that such a continuous