Paper Info
Title
An Essential Seventh-Order Weighted Compact Adaptive Scheme for Hyperbolic Conservation Laws
Abstract
A new seventh-order weighted compact adaptive scheme is proposed in this paper. The proposed reconstruction is inspired by the upwind compact scheme and the adaptive order weighted essentially non-oscillatory (WENO) scheme. The proposed seventh-order scheme is a convex combination of a linear seventh-order compact scheme and three linear third-order compact schemes. The reconstruction of the proposed scheme is based on the same stencil as the reconstruction of the original fifth-order weighted compact scheme. Various classical tests are presented to show the performance of the proposed numerical scheme. The numerical results of the proposed scheme are compared with those obtained with the original fifth-order compact WENO scheme, seventh-order compact WENO scheme and classical WENO schemes. The numerical results show that the proposed scheme preserves the designed seventh-order of accuracy in smooth regions and produces higher resolution solutions near shocks or discontinuities without numerical oscillations with less computational cost than the original weighted compact schemes.
Year
DOI
Venue
2021
10.1007/s10915-021-01664-z
JOURNAL OF SCIENTIFIC COMPUTING
Keywords
DocType
Volume
Hyperbolic conservation laws, Compact schemes, Weighted essentially non-oscillatory, High resolution, Adaptive order
Journal
89
Issue
ISSN
Citations 
3
0885-7474
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Yufeng Shi100.34
Yan Guo200.34