TY - JOUR
T1 - Entropy viscosity method for nonlinear conservation laws
AU - Guermond, Jean-Luc
AU - Pasquetti, Richard
AU - Popov, Bojan
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 Foundation Grant DMS-0713929, DMS-0811041 and 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 - 2011/5
Y1 - 2011/5
N2 - A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
AB - A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
UR - http://hdl.handle.net/10754/598201
UR - https://linkinghub.elsevier.com/retrieve/pii/S0021999110006583
UR - http://www.scopus.com/inward/record.url?scp=79953750438&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2010.11.043
DO - 10.1016/j.jcp.2010.11.043
M3 - Article
SN - 0021-9991
VL - 230
SP - 4248
EP - 4267
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 11
ER -