2018/03/26 by Raphaèle Herbin, Herbin, R., J.‐C. Latché +3 · 2 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Classical Physics (physics.class-ph) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Navier-Stokes equation solutions #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1803.09568
openalex publication_date 2018/03/26 · openalex created_date 2018/04/06 · openalex updated_date 2026/08/01
In this paper, we study the behaviour at low Mach number of numerical schemes based on staggered discretizations for the barotropic Navier-Stokes equations. Three time discretizations are considered: the implicit-in-time scheme and two non-iterative pressure correction schemes. The last two schemes differ by the discretization of the convection term: linearly implicit for the first one, so the resulting scheme is unconditionnally stable, and explicit for the second one, so the scheme is stable under a CFL condition involving the material velocity only. We rigorously prove that these three variants are asymptotic preserving in the following sense: for a given mesh and a given time step, a sequence of solutions obtained with a sequence of vanishing Mach numbers tend to a solution of a standard scheme for incompressible flows. This convergence result is obtained by mimicking the proof already known in the continuous case.