Low Mach number limit for degenerate Navier-Stokes equations in presence of strong stratification

2021/07/12 by Francesco Fanelli, Fanelli, Francesco, Ewelina Zatorska +1 · 3 citations
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · doi:10.48550/arxiv.2107.05157

Abstract

In this paper, we investigate the low Mach and low Froude numbers limit for the compressible Navier-Stokes equations with degenerate, density-dependent, viscosity coefficient, in the strong stratification regime. We consider the case of a general pressure law with singular component close to vacuum, and general ill-prepared initial data. We perform our study in the three-dimensional periodic domain. We rigorously justify the convergence to the generalised anelastic approximation, which is used extensively to model atmospheric flows.

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