A New ?-Adaptive Algorithm for Improving Weighted Compact Nonlinear Scheme with Applications

To improve the resolution and accuracy of high-order weighted compact nonlinear scheme (WCNS), a new ?-adaptive algorithm based on local smoothness indicators is proposed. The introduces global indicator to adjust value ? according flow characteristics. Specifically, increases in smooth regions, which can help cover up disparity sub-stencils make approach background linear scheme. As result, optimal order be achieved including critical points. While near discontinuities, decreases ?, thereby strengthening stencil selection mechanism further attenuating spurious oscillations. Meanwhile, makes schemes scale-invariant variables. results approximate dispersion relation (ADR) show that greatly reduce spectral errors medium low wavenumber range without inducing instability. Numerical indicate significantly small-scale structures suppress numerical oscillations discontinuities with only minor increment computational cost.