Geodesic
Accurate numerical discretizations of non-conservative hyperbolic systems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 1, pp. 187-206

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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.

DOI : 10.1051/m2an/2011044
Classification : 65M06, 35L65
Keywords: non-conservative products, numerical schemes 
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     title = {Accurate numerical discretizations of non-conservative hyperbolic systems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {187--206},
     publisher = {EDP-Sciences},
     volume = {46},
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     year = {2012},
     doi = {10.1051/m2an/2011044},
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     zbl = {1272.65064},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011044/}
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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

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