WCNS schemes and some recent developments

Weighted compact nonlinear schemes (WCNS) are a family of nonlinear shock capturing schemes that are suitable for solving problems with discontinuous solutions. The schemes are based on grids staggered by flux points and solution points, resulting in algorithms with the nonlinear interpolation step independent of the difference step. Thus, only linear difference operators are needed, such that geometric conservation law can be preserved easily, resulting in the preservation of freestream condition. In recent years, these schemes have attracted a lot of attention in the community of computational fluid dynamics. This paper intends to give a brief review of the basic algorithms of these schemes and present some related recent developments.