JS-type and Z-type weights for fourth-order central-upwind weighted essentially non-oscillatory schemes

TL;DR

This paper introduces JS-type and Z-type nonlinear weights for fourth-order central-upwind WENO schemes, improving accuracy and robustness by using a new smoothness indicator that considers the entire stencil's regularity.

Contribution

The paper develops a novel smoothness indicator and corresponding nonlinear weights for fourth-order central-upwind WENO schemes, enhancing their performance in shock capturing.

Findings

Improved accuracy in smooth regions.

Enhanced robustness and shock resolution.

Validated effectiveness in 1D and 2D problems.

Abstract

The central-upwind weighted essentially non-oscillatory (WENO) scheme introduces the downwind substencil to reconstruct the numerical flux, where the smoothness indicator for the downwind substencil is of critical importance in maintaining high order in smooth regions and preserving the essentially nonoscillatory behavior in shock capturing. In this study, we design the smoothness indicator for the downwind substencil by simply summing up all local smoothness indicators and taking the average, which includes the regularity information of the whole stencil. Accordingly the JS-type and Z-type nonlinear weights, based on simple local smoothness indicators, are developed for the fourth-order central-upwind WENO scheme. The accuracy, robustness, and high-resolution properties of our proposed schemes are demonstrated in a variety of one- and two-dimensional problems.