Further improvement of weighted compact nonlinear scheme using compact nonlinear interpolation

To further improve the resolution of weighted compact nonlinear schemes(WCNS), a new 7th-order compact nonlinear interpolation method is proposed on the same stencil as 5th-order CRWENO scheme. Proper nonlinear weights are developed based on the Y type nonlinear weights, the properties of which are further analyzed in this paper. It is found that the Y type nonlinear weights are equivalent to the original nonlinear weights with an adaptive ϵ, which has very small value near discontinuities and very large value in smooth regions. As a result, the new nonlinear scheme has good shock capturing ability and achieves optimal order of accuracy in smooth regions. A new characteristic projection method is put forward, which largely reduces the computation costs. Simulations of Lax problem, Osher-Shu problem, double Mach reflection problem, decay of homogenous turbulence, shock turbulence interaction and turbulent channel flow show that the new scheme captures shocks without obvious oscillations, has higher resolution than other schemes tested, has obvious advantage in distinguishing turbulence from shocks and has higher efficiency.