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

✍ Scribed by N.A. Adams; K. Shariff

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 631 KB
• Volume: 127
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0156

✦ Synopsis

ters. This problem is reflected in the fact that for wavetransport dominated problems a finer mesh spacing is re-A class of upwind-biased finite-difference schemes with a compact stencil is proposed in general form, suitable for the time-accuquired for an accurate representation of the dispersion rate direct numerical simulation of fluid-convection problems. relation than for an accurate approximation of the wave-These schemes give uniformly high approximation order and allow form itself at a time instant.

for a spectral-like wave resolution while dissipating non-resolved

This study emphasizes the distinction between order wavenumbers. When coupled with an essentially non-oscillatory of approximation and resolution. The first refers to a local scheme near discontinuities, the compact schemes become shockcapturing and their resolution properties are preserved. The deriva-Taylor expansion, and the local order of approximation of tion of the compact schemes is discussed in detail. Their convera spatial scheme is measured by the leading error term.

gence and resolution properties as well as numerical stability are

The second refers to a Fourier expansion, and we measure analyzed. Upwinding and coupling procedures are described. Applithe resolution of a scheme by the largest wavenumber cation examples for typical non-linear wave interaction problems are given. ᮊ 1996 Academic Press, Inc.

(normalized with the grid spacing h) of a single Fouriermode e Ϫix which can be accurately represented by the scheme. For general non-periodic solutions these criteria