An Optimised Five-Point-Stencil Weighted Compact Nonlinear Scheme for Hyperbolic Conservation Laws

Although weighted compact nonlinear scheme (WCNS) has been successfully applied to the simulation of complex configurations, due to the excessive dissipation, the scheme is still not suitable for many circumstances. In this article, an optimised five-point-stencil WCNS is proposed. On the one hand, by assembling two fourth-order sub-schemes, the background upwind scheme is optimised for low dissipation. On the other hand, with a specific function, the weighting strategy is optimised to enhance stability near discontinuities and further reduce dissipation in the smooth region. Finally, several benchmark problems are conducted to demonstrate the improved performance of the optimised scheme.