High-order entropy stable schemes for systems of conservation laws

Description

Systems of conservation laws modelling physical and engineering systems are equipped with an entropy formulation that provides stability estimates and selects the physically meaningful. We design arbitrarily high-order entropy stable schemes for a general system of conservation laws by combining entropy conservative fluxes with high-order numerical diffusion operators based on the ENO (essentially non-oscillatory) reconstruction. The schemes are applied to the shallow water equations and the Euler equations of gas dynamics. Ongoing work focuses on extension these high-order entropy stable schemes to unstructured grids and to the MHD equations.

Publications / Preprints or SAM-Reports

• Energy preserving and energy stable schemes for the shallow water equations, U. S. Fjordsholm, S. Mishra and E. Tadmor, Foundations of Computational Mathematics, Proc. FoCM, London Math. Soc. lecture notes, 363, 2009, 93-139.
• Well-balanced, energy stable schemes for the shallow water equations with varying topography, U. S. Fjordholm, S. Mishra and E. Tadmor, SAM report 2010-26, Journal of Computational Physics, To appear.
• An entropy stable ENO scheme, U. S. Fjordholm, S. Mishra and E. Tadmor, SAM report 2011-05.
  
  

Contacts

S. Mishra

U. Fjordholm