Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws

Authors:
Ulrik S. Fjordholm;Siddhartha Mishra;Eitan Tadmor
Affiliations:
ulrikf@sam.math.ethz.ch and smishra@sam.math.ethz.ch;-;tadmor@cscamm.umd.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2012

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Abstract

We design arbitrarily high-order accurate entropy stable schemes for systems of conservation laws. The schemes, termed TeCNO schemes, are based on two main ingredients: (i) high-order accurate entropy conservative fluxes and (ii) suitable numerical diffusion operators involving ENO reconstructed cell-interface values of scaled entropy variables. Numerical experiments in one and two space dimensions are presented to illustrate the robust numerical performance of the TeCNO schemes.