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

Guermond, Jean-Luc; Maier, Matthias; Popov, Bojan; Tomas, Ignacio

doi:10.1016/j.cma.2020.113608

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

Journal Article · Mon Mar 01 00:00:00 UTC 2021 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2020.113608· OSTI ID:1769910

Guermond, Jean-Luc ^[1]; Maier, Matthias ^[1]; ^[1]; Tomas, Ignacio ^[2]

Texas A & M Univ., College Station, TX (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Here, 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, i.e.

τ ≲ O (h) / V

where

V

is some reference velocity scale and

h

the typical meshsize.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); US Army Research Office (ARO); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1769910

Report Number(s):: SAND--2021-2077J; 693966

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 375; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Conservation equations
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Euler equations
Finite element method
High-order method
Hyperbolic systems
Invariant domains
Navier–Stokes equations

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

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