An improved third-order HWCNS scheme based on the multi-order candidates (MOC) weighting framework

To mitigate the order reduction of traditional third-order Z-type nonlinear weighted interpolation, a theoretical analysis method based on Taylor expansion is proposed for the order-of-magnitude relationships of smoothness indicators near critical points. The complete order-of-magnitude relationships for Z-type smoothness indicators are derived, revealing the underlying mechanism of accuracy degradation near critical points. Within the multi-order candidates (MOC) framework, an improved third-order HWCNS scheme is developed by introducing extended stencils, a new consistent high-order smoothness indicator (CHOSI), and a smoothness indicator order adaptive regulator (SIOAR). Theoretical analysis demonstrates that the proposed scheme maintains third-order accuracy in smooth regions and significantly reduces nonlinear errors while preserving robust shock-capturing capabilities. Numerical test cases verify that the scheme achieves high resolution, low dissipation, and high computational efficiency, offering new theoretical support and practical insights for applying high-order nonlinear schemes in engineering.