On the invariant region for compressible Euler equations with a general equation of state

Hailiang Liu; Ferdinand Thein

doi:10.3934/cpaa.2021084

Article Contents

2021, Volume 20, Issue 7&8: 2751-2763. Doi: 10.3934/cpaa.2021084

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On the invariant region for compressible Euler equations with a general equation of state

Hailiang Liu^1, , and
Ferdinand Thein^2,

1.
Iowa State University, Mathematics Department, Ames, IA 50011, USA
2.
Otto-von-Guericke-Universität, Universitätsplatz 2, Magdeburg, 39106, Germany

^* Corresponding author
^* Corresponding author

Dedicated to Professor Shuxing Chen on the occasion of his 80th birthday

Received: February 2021

Revised: April 2021

Early access: May 2021

Published: August 2021

Hailiang Liu was partially supported by the National Science Foundation under Grant DMS1812666

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Abstract

The state space for solutions of the compressible Euler equations with a general equation of state is examined. An arbitrary equation of state is allowed, subject only to the physical requirements of thermodynamics. An invariant region of the resulting Euler system is identified and the convexity property of this region is justified by using only very minimal thermodynamical assumptions. Finally, we show how an invariant-region-preserving (IRP) limiter can be constructed for use in high order finite-volume type schemes to solve the compressible Euler equations with a general constitutive relation.

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Mathematics Subject Classification: Primary: 35L65, 76N15; Secondary: 65M08.

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