Entropy viscosity method for nonlinear conservation laws

abstract

• 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.

authors

• Popov, Bojan

published proceedings

• JOURNAL OF COMPUTATIONAL PHYSICS

author list (cited authors)

• Guermond, J., Pasquetti, R., & Popov, B.

citation count

• 230

complete list of authors

• Guermond, Jean-Luc||Pasquetti, Richard||Popov, Bojan

publication date

• May 2011

publisher

• Elsevier  Publisher

published in

• Journal of Computational Physics  Journal

keywords

• Central Schemes
• Conservation Laws
• Entropy Viscosity
• Euler Equations
• Finite Elements
• Fourier Method
• Godunov Schemes
• Spectral Elements

Digital Object Identifier (DOI)

• 10.1016/j.jcp.2010.11.043

start page

• 4248

end page

• 4267

volume

• 230

issue

• 11

URL

• http://dx.doi.org/10.1016/j.jcp.2010.11.043