A high performance fifth‐order multistep WENO scheme

Abstract

Summary Many efforts have been made to improve the accuracy of the conventional weighted essentially nonoscillatory (WENO) scheme at transition points (connecting a smooth region and a discontinuity point). This paper analyzes these works and further develops a more effective multistep WENO scheme. Theoretical analysis and numerical results show that the new scheme not only improves the accuracy by one order higher than the traditional fifth‐order WENO schemes at transition point but also maintains the fifth‐order accuracy in smooth regions even at critical point where the first derivative vanishes.