A novel nonlinear spectral difference scheme with adaptive linear weights

Abstract

Abstract This paper presents a nonlinear spectral difference (SD) scheme with adaptive linear weights for solving hyperbolic conservation laws. The proposed scheme enhances the traditional SD method by incorporating a nonlinear weighting strategy that adaptively adjusts linear weights based on local solution smoothness. The scheme maintains fifth-order accuracy in smooth regions while effectively capturing discontinuities. The numerical framework is validated through a series of benchmark problems, and the results demonstrate the proposed nonlinear scheme’s high-order accuracy, robustness, and ability to resolve complex flow structures without spurious oscillations. The adaptive linear weighting strategy ensures stability and accuracy across a wide range of flow conditions, making the scheme suitable for high-resolution simulations in computational fluid dynamics.