A high performance fifth‐order multistep WENO scheme. (7th June 2019)

• Record Type: Journal Article
• Authors: Zeng, Fangjun; Shen, Yiqing; Liu, Shengping; Liu, Li
• Is Part Of: International journal for numerical methods in fluids. Volume 91:Number 4(2019)
• Page Start: 159
• Page End: 182
• Publication Date: 2019-06-07
• Subjects: critical point -- high performance -- low‐dissipation -- multistep WENO scheme -- transition point; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4747
• Languages: English
• ISSNs: 0271-2091

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. Abstract : In this paper, a high performance fifth‐order multistep WENO scheme is constructed. The new scheme improves the accuracy by one order higher than the traditional fifth‐order WENO schemes at transition point, and its weights satisfy the necessary and sufficient conditions for fifth‐order convergence in smooth regions including critical points. Numerical results show that the new scheme has ENO and low dissipation properties near discontinuities and is more efficient than the original multistep WENO scheme.