High‐resolution mapping type WENO‐Z schemes for solving compressible flow

Abstract

SummaryThis paper presents a new WENO‐Z scheme (WENO‐MZ) that incorporates a mapping function to enhance the weights of the less smooth sub‐stencils. The mapping function uses an innovative approach to modify the weight ratio of the less smooth sub‐stencil to the smooth stencil. In addition, we present the WENO‐MD scheme, which is a further development of the WENO‐MZ scheme that incorporates a modifier function. The WENO‐MD scheme shows improvements over the WENO‐MZ scheme by achieving an improved optimal order at critical points in higher orders and by increasing the proportion of less smooth sub‐stencils. Theoretical and numerical experiments have shown that the newly developed methods have improved shock capture capabilities and resolution compared to WENO‐JS, WENO‐Z, WENO‐M, WENO‐D, and WENO‐AIM, and also lead to significant computational time savings compared to WENO‐M and WENO‐AIM.