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

Authors:
Travis C. Fisher;Mark H. Carpenter
Affiliations:
Computational AeroSciences Branch, NASA Langley Research Center, Hampton, VA 23681, USA and School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA;Computational AeroSciences Branch, NASA Langley Research Center, Hampton, VA 23681, USA
Venue:
Journal of Computational Physics
Year:
2013

Citing 31
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Abstract

Nonlinear entropy stability is used to derive provably stable high-order finite difference operators including boundary closure stencils, for the compressible Navier-Stokes equations. A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks. Viscous terms are approximated using conservative, entropy stable, narrow-stencil finite difference operators. The efficacy of the new discrete operators is demonstrated using both smooth and discontinuous test cases.