Analysis of an alternative Navier-Stokes system: Weak entropy solutions and a convergent numerical scheme

2022/03/04 by Svärd, Magnus
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2203.02159

Abstract

We consider an alternative Navier-Stokes model for compressible viscous ideal gases, originally proposed in \citeSvard18. We derive a priori estimates that are sufficiently strong to support a weak entropy solution of the system. Guided by these estimates, we propose a finite volume scheme, derive the analogous estimates and demonstrate grid convergence towards a weak entropy solution. Furthermore, this existence proof is valid for "large" initial data and no a priori assumptions on the solution are needed.

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