Paper Info
Title
Improving Accuracy Of The Fifth-Order Weno Scheme By Using The Exponential Approximation Space
Abstract
The aim of this study is to develop a novel WENO scheme that improves the performance of the well-known fifth-order WENO methods. The approximation space consists of exponential polynomials with a tension parameter that may be optimized to fit the the specific feature of the data, yielding better results compared to the polynomial approximation space. However, finding an optimal tension parameter is a very important and difficult problem, indeed a topic of active research. In this regard, this study introduces a practical approach to determine an optimal tension parameter by taking into account the relationship between the tension parameter and the accuracy of the exponential polynomial interpolation under the setting of the fifth-order WENO scheme. As a result, the proposed WENO scheme attains an improved order of accuracy (that is, sixth-order) better than other fifth-order WENO methods without loss of accuracy at critical points. A detailed analysis is provided to verify the improved convergence rate. Further, we present modified nonlinear weights based on an L-1-norm approach along with a new global smoothness indicator. The proposed nonlinear weights reduce numerical dissipation significantly, while attaining better resolution in smooth regions. Some experimental results for various benchmark test problems are presented to demonstrate the ability of the new scheme.
Year
DOI
Venue
2021
10.1137/20M1317396
SIAM JOURNAL ON NUMERICAL ANALYSIS
Keywords
DocType
Volume
hyperbolic conservation laws, WENO scheme, exponential polynomial interpolation, tension parameter, order of accuracy, smoothness indicator
Journal
59
Issue
ISSN
Citations 
1
0036-1429
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Youngsoo Ha14510.08
Chang Ho Kim29442.60
Chi-Wang Shu34053540.35
Jungho Yoon418129.08