Low Mach number limit of a pressure correction MAC scheme for compressible barotropic flows

2017/03/03 by Raphaèle Herbin, Herbin, Raphaele, J.‐C. Latché +3
Engineering · Earth and Planetary Sciences · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Tropical and Extratropical Cyclones Research #Navier-Stokes equation solutions

paper · doi:10.48550/arxiv.1703.01231

Abstract

We study the incompressible limit of a pressure correction MAC scheme [3] for the unstationary compressible barotropic Navier-Stokes equations. Provided the initial data are well-prepared, the solution of the numerical scheme converges, as the Mach number tends to zero, towards the solution of the classical pressure correction inf-sup stable MAC scheme for the incompressible Navier-Stokes equations.

Related

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• Low Mach number limit for the compressible Navier-Stokes equation with a stationary force
• Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations
• Improved error estimates for the finite volume and the MAC schemes for the compressible Navier-Stokes system
• Low Mach number limit of the global solution to the compressible Navier-Stokes system for large data in the critical Besov space