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

Access to Document

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

Cite this

@inbook{8eddefe1c8f342509853cd928d68323a,

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.",

author = "Guermond, {J. L.} and R. Pasquetti",

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.",

year = "2010",

month = sep,

day = "17",

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

language = "English (US)",

isbn = "9783642153365",

pages = "411--418",

booktitle = "Spectral and High Order Methods for Partial Differential Equations",

publisher = "Springer Nature",

}

TY - CHAP

T1 - Entropy Viscosity Method for High-Order Approximations of Conservation Laws

AU - Guermond, J. L.

AU - Pasquetti, R.

N1 - 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.

PY - 2010/9/17

Y1 - 2010/9/17

N2 - 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.

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.

UR - http://hdl.handle.net/10754/598200

UR - http://link.springer.com/10.1007/978-3-642-15337-2_39

UR - http://www.scopus.com/inward/record.url?scp=78651535060&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-15337-2_39

DO - 10.1007/978-3-642-15337-2_39

M3 - Chapter

SN - 9783642153365

SP - 411

EP - 418

BT - Spectral and High Order Methods for Partial Differential Equations

PB - Springer Nature

ER -

Entropy Viscosity Method for High-Order Approximations of Conservation Laws

Abstract

Access to Document

Other files and links

Fingerprint

Cite this