A Convergent Numerical Scheme for the Compressible Navier--Stokes Equations

Abstract

In this paper, the three-dimensional compressible Navier--Stokes equations are considered on a periodic domain. We propose a semidiscrete numerical scheme and derive a priori bounds that ensure that the resulting system of ordinary differential equations (ODEs) is solvable for any $h>0$. An a posteriori observation that density remains uniformly bounded away from 0 will establish that a subsequence of the numerical solutions converges to a specific form of weak solution of the compressible Navier--Stokes equations.