Accurate numerical discretizations of non-conservative hyperbolic systems
Seminar for Applied Mathematics, ETH
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