A High-Resolution Hybrid Compact-ENO Scheme for Shock-Turbulence Interaction Problems

A class of upwind-biased finite-difference schemes with a compact stencil is proposed in general form, suitable for the time-accurate direct numerical simulation of fluid-convection problems. These schemes give uniformly high approximation order and allow for a spectral-like wave resolution while dissipating non-resolved wavenumbers. When coupled with an essentially non-oscillatory scheme near discontinuities, the compact schemes become shock-capturing and their resolution properties are preserved. The derivation of the compact schemes is discussed in detail. Their convergence and resolution properties as well as numerical stability are analyzed. Upwinding and coupling procedures are described. Application examples for typical non-linear wave interaction problems are given.

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