Second-order invariant domain preserving approximation of the compressible Navier--Stokes equations

TL;DR

This paper introduces a second-order accurate, semi-implicit numerical method for the compressible Navier-Stokes equations that preserves physical invariants and adheres to standard CFL conditions.

Contribution

It develops a fully discrete, invariant domain preserving scheme that is second-order accurate in both time and space for compressible Navier-Stokes equations.

Findings

Method guarantees invariant domain preservation.

Achieves second-order accuracy in time and space.

Operates under standard CFL condition.

Abstract

We present a fully discrete approximation technique for the compressible Navier-Stokes equations that is second-order accurate in time and space, semi-implicit, and guaranteed to be invariant domain preserving. The restriction on the time step is the standard hyperbolic CFL condition, ie $\tau \lesssim \mathcal{O}(h)/V$ where $V$ is some reference velocity scale and $h$ the typical meshsize.