ADM‐WENO scheme and its application in compressible mixing flows

High order schemes, which are widely used in DNS and LES, received increasing attention in recent years with a number of variants being developed. However most of these schemes have difficulties in achieving high order accuracy near the boundary points. In order to solve this problem, the analytical discrete method (ADM) is proposed and presented in this paper. In addition, this method is convenient to construct the higher order WENO (weighted essentially non‐oscillatory) scheme. Application of the ADM‐WENO scheme to shock‐tube problems and compressible mixing flows has shown it is robust and accurate in both shock‐capturing and complex flow structures detection.