基于映射的模板光滑探测子的三阶WENO格式

王亚辉; 郭城; 杜玉龙

doi:10.21656/1000-0887.450150

基于映射的模板光滑探测子的三阶WENO格式

doi: 10.21656/1000-0887.450150

1. 郑州师范学院数学与统计学院，郑州 450044;
2. 江苏海洋大学理学院，江苏连云港 222005

基金项目:

国家自然科学基金(12071470)；河南省高等学校重点科研项目(22B110020)

河南省自然科学基金(252300420394)

详细信息

作者简介:
王亚辉(1991—)，男，博士(通讯作者. E-mail: hlg_cfd2014@163.com);郭城(1980—)，男，硕士(E-mail: gc_scv@163.com);杜玉龙(1988—)，男，博士(E-mail: kunyu0918@163.com).

通讯作者:
王亚辉(1991—)，男，博士(通讯作者. E-mail: hlg_cfd2014@163.com)

中图分类号: O357.41
计量
- 文章访问数: 17
- HTML全文浏览量: 5
- PDF下载量: 3
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-21
- 修回日期: 2024-07-06
- 网络出版日期: 2025-04-02
- 刊出日期: 2025-03-01

A 3rd-Order WENO Scheme for Stencil Smoothness Indicators Based on Mapping

1. School of Mathematics and Statistics, Zhengzhou Normal University, Zhengzhou 450044, P.R.China;
2. School of Science, Jiangsu Ocean University, Lianyungang, Jiangsu 222005, P.R.China

Funds:

The National Science Foundation of China(12071470)

摘要

摘要: 加权本质无振荡(weighted essentially non-oscillatory,WENO)格式能否具有低耗散特性及高分辨率特性,关键在于光滑探测子的构造.该文针对三阶WENO格式的光滑探测子进行修正,通过最光滑的探测子,构造出了一个关于子模板光滑探测子的映射函数.在该函数作用下,减小了欠光滑模板的光滑探测子,进而增大了欠光滑模板的非线性权重.这明显地降低了格式的数值耗散,提高了格式的分辨率.一系列数值测试表明，基于映射的模板光滑探测子的三阶WENO格式比传统的三阶WENO-JS3和WENO-Z3格式具有更高的分辨率.
- 双曲守恒律 /
- WENO /
- 映射 /
- 光滑探测子 /
- 非线性权
Abstract: The key to whether the WENO scheme can achieve optimal convergence accuracy and maintain essential no-oscillation characteristics near discontinuities lies in the construction of smoothness indicators. The smoothness indicator of the 3rd-order WENO scheme was modified through the construction of a mapping function to correct the smoothness indicators on each candidate stencil with the smoothest indicator. Under the influence of this mapping function, the smoothness indicator of the under-smooth stencil was reduced, thereby the nonlinear weight of the under-smooth stencil was increased. Then the numerical dissipation of the scheme was significantly lowered and its resolution was improved. A series of numerical examples demonstrate that, the new 3rd-order WENO scheme for smoothness indicators based on mapping has higher resolution than the classical WENO-JS3 and WENO-Z3 schemes.
- hyperbolic conservation law /
- WENO /
- mapping /
- smoothness indicator /
- nonlinear weight

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参考文献(27)

[2]HARTEN A, ENGQUIST B, OSHER S, et al. Uniformly high order accurate essentially non-oscillatory schemes, Ⅲ[J].Journal of Computational Physics,1987,71(2): 231-303.〖JP〗

LIU X D, OSHER S, CHAN T. Weighted essentially non-oscillatory schemes[J].Journal of Computational Physics,1994,115(1): 200-212.

[3]JIANG G S, SHU C W. Efficient implementation of weighted ENO schemes[J].Journal of Computational Physics,1996,126(1): 202-228.

[4]SHU C W, OSHER S. Efficient implementation of essentially non-oscillatory shock-capturing schemes, Ⅱ[J].Journal of Computational Physics,1989,83(1): 32-78.

[5]HENRICK A K, ASLAM T D, POWERS J M. Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points[J].Journal of Computational Physics,2005,207(2): 542-567.

[6]BORGES R, CARMONA M, COSTA B, et al. An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws[J].Journal of Computational Physics,2008,227(6): 3191-3211.

[7]HA Y, KIM C H, LEE Y J, et al. An improved weighted essentially non-oscillatory scheme with a new smoothness indicator[J].Journal of Computational Physics,2013,232(1): 68-86.

[8]FAN P, SHEN Y Q, TIAN B L, et al. A new smoothness indicator for improving the weighted essentially non-oscillatory scheme[J].Journal of Computational Physics,2014,269: 329-354.

[9]YAN Z G, LIU H Y, MAO M L, et al. New nonlinear weights for improving accuracy and resolution of weighted compact nonlinear scheme[J].Computers & Fluids,2016,127: 226-240.

[10]KIM C H, HA Y S, YOON J H. Modified non-linear weights for fifth-order weighted essentially non-oscillatory schemes[J].Journal of Scientific Computing,2016,67(1): 299-323.

[11]CASTRO M, COSTA B, DON W S. High order weighted essentiallynon-oscillatory WENO-Z schemes for hyperbolic conservation laws[J].Journal of Computational Physics,2011,230(5): 1766-1792.

[12]ARNDIGA F, BAEZA A, BELDA A M, et al. Analysis of WENO schemes for full and global accuracy[J].SIAM Journal on Numerical Analysis,2011,49(2): 893-915.

[13]王亚辉. 求解双曲守恒律方程的三阶修正模板WENO格式[J]. 应用数学和力学, 2022,43(2): 224-236. (WANG Yahui. A 3rd-order modified stencil WENO scheme for solution of hyperbolic conservation law equations[J].Applied Mathematics and Mechanics,2022,43(2): 224-236. (in Chinese))

[14]WANG Y H, DU Y L, ZHAO K L, et al. Modified stencil approximations for fifth-order weighted essentially non-oscillatory schemes[J].Journal of Scientific Computing,2019,81(2): 898-922.

[15]WANG Y H, DU Y L, ZHAO K L, et al. A new 6th-order WENO scheme with modified stencils[J].Computers & Fluids,2020,208: 104625.

[16]WANG Y H. Improved weighted essentially non-oscillatory schemes with modified stencil approximation[J].Computational and Applied Mathematics,2023,42(2): 82.

[17]ZENG F J, SHEN Y Q, LIU S P. A perturbational weighted essentially non-oscillatory scheme[J].Computers & Fluids,2018,172: 196-208.

[18]WU X, ZHAO Y. A high-resolution hybrid scheme for hyperbolic conservation laws[J].International Journal for Numerical Methods in Fluids,2015,78(3): 162-187.

[19]WU X, LIANG J, ZHAO Y. A new smoothness indicator for third-order WENO scheme[J].International Journal for Numerical Methods in Fluids,2016,81(7): 451-459.

[20]XU W, WU W. An improved third-order WENO-Z scheme[J].Journal of Scientific Computing,2018,75(3): 1808-1841.

[21]WANG Y H, DU Y L, ZHAO K L, et al. A low-dissipation third-order weighted essentially nonoscillatory scheme with a new reference smoothness indicator[J].International Journal for Numerical Methods in Fluids,2020,92(9): 1212-1234.

[22]王亚辉. 基于新的参考光滑性指示子的改进的三阶WENO格式[J]. 应用数学和力学, 2022,43(7): 802-815. (WANG Yahui. An improved 3rd-order WENO scheme based on a new reference smoothness indicator[J].Applied Mathematics and Mechanics,2022,43(7): 802-815. (in Chinese))

[23]徐维铮, 吴卫国. 三阶WENO-Z格式精度分析及其改进格式[J]. 应用数学和力学, 2018,39(8): 946-960. (XU Weizheng, WU Weiguo. Precision analysis of the 3rd-order WENO-Z scheme and its improved scheme[J].Applied Mathematics and Mechanics,2018,39(8): 946-960. (in Chinese))

[24]LAX P D. Weak solutions of nonlinear hyperbolic equations and their numerical computation[J].Communications on Pure and Applied Mathematics,1954,7(1): 159-193.

[25]SOD G A. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws[J].Journal of Computational Physics,1978,27(1): 1-31.

[26]WANG Y H, GUO C. Improved third-order WENO scheme with a new reference smoothness indicator[J].Applied Numerical Mathematics,2023,192: 454-472.

[27]WOODWARD P, COLELLA P. The numerical simulation of two-dimensional fluid flow with strong shocks[J].Journal of Computational Physics,1984,54(1): 115-173.

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