Analysis of super compact finite difference method and application to simulation of vortex-shock interaction

Turbulence and aeroacoustic noise high-order accurate schemes are required, and preferred, for solving complex flow fields with multi-scale structures . In this paper a super compact finite difference method (SCFDM) is present ed, the accuracy is analysed and the method is compared with a sixth-order traditional and compact finite difference approximation. The comparison sho ws that the sixth-order accurate super compact method has higher resolving efficiency. The sixth-order super compact method, with a three-stage Runge- Kutta method for approximation of the compressible Navier-Stokes equations, is used to solve the complex flow structures induced by vortex-shock inter actions. The basic nature of the near-field sound generated by interaction is studied. Copyright (C) 2001 John Wiley & Sons, Ltd.