IMPROVING ACCURACY OF THE FIFTH-ORDER WENO SCHEME BY USING THE EXPONENTIAL APPROXIMATION SPACE
- 주제(키워드) hyperbolic conservation laws , WENO scheme , exponential polynomial interpolation , tension parameter , order of accuracy , smoothness indicator
- 주제(기타) Mathematics, Applied
- 설명문(일반) [Ha, Youngsoo] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea; [Kim, Chang Ho] Konkuk Univ, Dept Comp Engn, Glocal Campus, Chungju 27478, South Korea; [Yang, Hyoseon] Michigan State Univ, Dept Computat Math Sci & Engn, E Lansing, MI 48824 USA; [Yoon, Jungho] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 SIAM PUBLICATIONS
- 발행년도 2021
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000181484
- 본문언어 영어
- Published As http://dx.doi.org/10.1137/20M1317396
초록/요약
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.
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