Entropy Viscosity Method for High-Order Approximations of Conservation Laws

J. L. Guermond; R. Pasquetti

doi:10.1007/978-3-642-15337-2_39

Entropy Viscosity Method for High-Order Approximations of Conservation Laws

J. L. Guermond, R. Pasquetti

Research output: Chapter in Book/Report/Conference proceeding › Chapter

21 Scopus citations

Abstract

A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.

Original language	English (US)
Title of host publication	Spectral and High Order Methods for Partial Differential Equations
Publisher	Springer Nature
Pages	411-418
Number of pages	8
ISBN (Print)	9783642153365
DOIs	https://doi.org/10.1007/978-3-642-15337-2_39
State	Published - Sep 17 2010
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This material is based upon work supported by the National Science Foun-dation grant DMS-0510650 and DMS-0811041 and partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST)
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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title = "Entropy Viscosity Method for High-Order Approximations of Conservation Laws",

abstract = "A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the {"}KPP rotating wave{"} and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. {\textcopyright} 2011 Springer.",

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doi = "10.1007/978-3-642-15337-2_39",

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AU - Pasquetti, R.

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AB - A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.

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PB - Springer Nature

ER -

Entropy Viscosity Method for High-Order Approximations of Conservation Laws

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