A skew-symmetric energy and entropy stable formulation of the compressible Euler equations

Jan Nordström

doi:10.1016/j.jcp.2022.111573

A skew-symmetric energy and entropy stable formulation of the compressible Euler equations

Jan Nordström

Mathematics and Applied Mathematics

Linköping University

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric form and show how to obtain energy and entropy estimates. Finally we show that the skew-symmetric formulation lead to energy and entropy stable discrete approximations if the scheme is formulated on summation-by-parts form.

Original language	English
Article number	111573
Journal	Journal of Computational Physics
Volume	470
DOIs	https://doi.org/10.1016/j.jcp.2022.111573
Publication status	Published - 1 Dec 2022

Keywords

Compressible Euler equations
Energy stability
Entropy stability
Nonlinear hyperbolic problems
Skew-symmetric form
Summation-by-parts

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.jcp.2022.111573

Cite this

@article{3b261b01be964de3b4afaa8c7daab2fa,

title = "A skew-symmetric energy and entropy stable formulation of the compressible Euler equations",

abstract = "We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric form and show how to obtain energy and entropy estimates. Finally we show that the skew-symmetric formulation lead to energy and entropy stable discrete approximations if the scheme is formulated on summation-by-parts form.",

keywords = "Compressible Euler equations, Energy stability, Entropy stability, Nonlinear hyperbolic problems, Skew-symmetric form, Summation-by-parts",

author = "Jan Nordstr{\"o}m",

note = "Publisher Copyright: {\textcopyright} 2022 The Author(s)",

year = "2022",

month = dec,

day = "1",

doi = "10.1016/j.jcp.2022.111573",

language = "English",

volume = "470",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - A skew-symmetric energy and entropy stable formulation of the compressible Euler equations

AU - Nordström, Jan

PY - 2022/12/1

Y1 - 2022/12/1

N2 - We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric form and show how to obtain energy and entropy estimates. Finally we show that the skew-symmetric formulation lead to energy and entropy stable discrete approximations if the scheme is formulated on summation-by-parts form.

AB - We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric form and show how to obtain energy and entropy estimates. Finally we show that the skew-symmetric formulation lead to energy and entropy stable discrete approximations if the scheme is formulated on summation-by-parts form.

KW - Compressible Euler equations

KW - Energy stability

KW - Entropy stability

KW - Nonlinear hyperbolic problems

KW - Skew-symmetric form

KW - Summation-by-parts

UR - http://www.scopus.com/inward/record.url?scp=85137152171&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2022.111573

DO - 10.1016/j.jcp.2022.111573

M3 - Article

AN - SCOPUS:85137152171

SN - 0021-9991

VL - 470

JO - Journal of Computational Physics

JF - Journal of Computational Physics

M1 - 111573

ER -

A skew-symmetric energy and entropy stable formulation of the compressible Euler equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this