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.
Mots-clés : non-conservative products, numerical schemes
@article{M2AN_2012__46_1_187_0,
author = {Fjordholm, Ulrik Skre and Mishra, Siddhartha},
title = {Accurate numerical discretizations of non-conservative hyperbolic systems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {187--206},
publisher = {EDP-Sciences},
volume = {46},
number = {1},
year = {2012},
doi = {10.1051/m2an/2011044},
mrnumber = {2846371},
zbl = {1272.65064},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2011044/}
}
TY - JOUR AU - Fjordholm, Ulrik Skre AU - Mishra, Siddhartha TI - Accurate numerical discretizations of non-conservative hyperbolic systems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 187 EP - 206 VL - 46 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011044/ DO - 10.1051/m2an/2011044 LA - en ID - M2AN_2012__46_1_187_0 ER -
%0 Journal Article %A Fjordholm, Ulrik Skre %A Mishra, Siddhartha %T Accurate numerical discretizations of non-conservative hyperbolic systems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 187-206 %V 46 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011044/ %R 10.1051/m2an/2011044 %G en %F M2AN_2012__46_1_187_0
Fjordholm, Ulrik Skre; Mishra, Siddhartha. Accurate numerical discretizations of non-conservative hyperbolic systems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 1, pp. 187-206. doi : 10.1051/m2an/2011044. http://www.numdam.org/articles/10.1051/m2an/2011044/
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