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High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains. (English) Zbl 1349.65293
Summary: 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.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
Software:
SageMath
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