Weighted Compact Scheme for Shock Capturing

Abstract

Abstract In this paper 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 achieve 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 the new scheme is very promising and successful.