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

2020; Elsevier BV; Volume: 375; Linguagem: Inglês

10.1016/j.cma.2020.113608

1879-2138

Jean‐Luc Guermond, Matthias Maier, Bojan Popov, Ignacio Tomaš,

Numerical methods for differential equations

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.