WEIGHTED COMPACT SCHEME FOR SHOCK CAPTURING

INTRODUCTIONRecently compact schemes have been widelyused in the simulation of complex flows,espe-cially in the directnumerical simulation of turbu-lent flows1～ 2 ] . Standard finite differenceschemes have explicit forms and need to be atleastone pointwider than the desired approxima-tion order. It is also difficult to find suitable andstable boundary closure for high order schemes.Compared to the standard finite difference ap-proximations,the compact schemes can achievehigher order acc…

WEIGHTED COMPACT SCHEME FOR SHOCK CAPTURING

A new class of finite difference schemes--the weighted compact schemes are proposed. According to the idea of the WENO schemes, the weighted compact scheme is constructed by a combination of the approximations of derivatives on candidate stencils with properly assigned weights so that the non oscillatory property is achieved when discontinuities appear. The primitive function reconstruction method of ENO schemes is applied to obtain the conservative form of the weighted compact scheme. This new scheme not only preserves the characteristic of standard compact schemes and achieves high order accuracy and high resolution using a compact stencil, but also can accurately capture shock waves and discontinuities without oscillation. Numerical examples show that the new scheme is very promising and successful.