| Issue |
ESAIM: M2AN
Volume 46, Number 1, January-February 2012
|
|
|---|---|---|
| Page(s) | 187 - 206 | |
| DOI | https://doi.org/10.1051/m2an/2011044 | |
| Published online | 03 October 2011 | |
Accurate numerical discretizations of non-conservative hyperbolic systems
Seminar for Applied Mathematics, ETH
Zürich, Rämistrasse
101, 8092
Zürich,
Switzerland
;
ulrikf@sam.math.ethz.ch
Received: 7 August 2010
Revised: 26 April 2011
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.
Mathematics Subject Classification: 65M06 / 35L65
Key words: Non-conservative products / numerical schemes
© EDP Sciences, SMAI, 2011
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