ADVANCES IN HIGH-ORDER ACCURATE WEIGHTED COMPACT NONLINEAR SCHEMES

The progress in the theoretical analysis of high-order accurate weighted compact nonlinear schemes (WCNS)and applications to the complicated flows is summarized in this paper.The development of high-order schemes is reviewed,focusing on WCNS.WCNS are analyzed with Fourier method and asymptotic stability theory.Some explicit WCNS are used to solve multi-dimensional complicated flows.