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

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.

References in corpus (4)

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Cited by in corpus (5)

• Positivity-Preserving Entropy-Based Adaptive Filtering for Discontinuous Spectral Element Methods
• A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations
• On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations
• Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state
• Structure-preserving finite-element schemes for the Euler-Poisson equations