High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains

Abstract

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrowstencil finite difference approach is used to approximate viscous terms.

DOI: 10.1016/j.jcp.2013.06.014

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@article{Fisher2013HighorderES, title={High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains}, author={Travis C. Fisher and Mark H. Carpenter}, journal={J. Comput. Physics}, year={2013}, volume={252}, pages={518-557} }