A reduced-dissipation WENO scheme with automatic dissipation adjustment

Abstract

In this paper, we propose a novel modification to the WENO-family schemes to reduce its intrinsic dissipation. In this work, we focus on the WENO5 scheme, which is rewritten in terms of a central plus a dissipative part, and then, the dissipation is controlled based on the flow physics. This is achieved by using the automatic dissipation adjustment (ADA) method in an a posteriori approach. This methodology allows us to greatly increase the accuracy of the original scheme at the same time ensure the robustness of the numerical method. The accuracy and robustness of the proposed scheme are tested by several selected numerical benchmarks.