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

Abstract

We consider an alternative Navier–Stokes model for compressible viscous ideal gases, originally proposed in [M. Svärd, A new Eulerian model for viscous and heat conducting compressible flows, Physica A 506 (2018) 350–375.] 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.