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Accurate numerical discretizations of non-conservative hyperbolic systems

Published online by Cambridge University Press:  03 October 2011

Ulrik Skre Fjordholm  and
Siddhartha Mishra
Ulrik Skre Fjordholm
Affiliation:
Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland. ulrikf@sam.math.ethz.ch . smishra@sam.math.ethz.ch ;
Siddhartha Mishra
Affiliation:
Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland. ulrikf@sam.math.ethz.ch . smishra@sam.math.ethz.ch ;
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Abstract

We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating the robustness of this approach are presented.

Keywords

Non-conservative productsnumerical schemes
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 1 , January 2012 , pp. 187 - 206
Copyright
© EDP Sciences, SMAI, 2011

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