An Improved Third-Order Hybrid Weighted Compact Nonlinear Scheme Based on Exponential Polynomials

Abstract

Translate Article

In this study, we propose a novel weighted compact nonlinear scheme that enhances the performance of the known third-order scheme and addresses the issue of inconsistent accuracy between its nonlinear reconstruction step and compact weighting step. To more accurately approximate steep gradients and high oscillations, an interpolation method based on exponential polynomials with a shape parameter is introduced. Specifically, a method for selecting locally optimised parameters that achieve fourth-order accuracy at non-critical points is proposed. Additionally, we introduce a smoothness indicator based on exponential polynomials, which increases the nonlinear weights of less smooth sub-stencils and improves the resolution of the scheme. To demonstrate the optimal numerical accuracy and the shock-capturing capabilities of the proposed scheme, numerical results are presented.