WCNS is weighted compact nonlinear scheme. Nonomura, Iizuka and Fujii showed the very good property of this scheme on the freestream preservation on the wavy grid compared with WENO.
Nonomura, Iizuka and Fujii also developed higher-order WCNS. Now, more efficient implementation of WCNS is investigated.
Importnat
High-order WCNS was presented in AIAA-paper 2007-893. However this paper has several typos in coefficients in WCNS. For the accurate coefficients, see this document.
Now, Goto, Nonomura and Fujii use relative limiter and absolute limiter for smooth indicator. This can help to reduce the computational costs and improve the resolution.