改进的三阶WENO-Z+格式及其应用

doi:10.19596/j.cnki.1001-246x.7575

计算物理 ›› 2018, Vol. 35 ›› Issue (1): 13-21.DOI: 10.19596/j.cnki.1001-246x.7575

改进的三阶WENO-Z+格式及其应用

徐维铮^1,2, 孔祥韶^1,2, 吴卫国^1,2

1. 武汉理工大学高性能舰船技术教育部重点实验室, 武汉 430063;
2. 武汉理工大学交通学院, 船舶、海洋与结构工程系, 武汉 430063

收稿日期:2016-11-10 修回日期:2017-03-09 出版日期:2018-01-25 发布日期:2018-01-25
通讯作者: 孔祥韶(1983-),男,博士,硕士生导师,主要从事舰船结构抗爆、抗冲击研究等,E-mail:kongxs@whut.edu.cn
作者简介:徐维铮(1991-),男,博士,主要从事爆炸波数值计算研究等,E-mail:xuweizheng@whut.edu.cn;吴卫国(1960-),男,教授,博导,主要从事结构动力学研究等,E-mail:mailjt@163.com
基金资助:
国防基础研究项目（B1420133057）及国家自然科学基金项目（51409202）资助

An Improved Third-order WENO-Z+3 Scheme and Its Application

XU Weizheng^1,2, KONG Xiangshao^1,2, WU Weiguo^1,2

1. Key Laboratory of High Performance Ship Technology of Ministry of Education, Wuhan University of Technology, Wuhan 430063, China;
2. Departments of Naval Architecture, Ocean and Structural Engineering, School of Transportation, Wuhan University of Technology, Wuhan, 430063, China

Received:2016-11-10 Revised:2017-03-09 Online:2018-01-25 Published:2018-01-25

摘要/Abstract

摘要： 为改善三阶WENO格式的耗散特性，提高其对流场结构的分辨率，在三阶WENO-Z+格式（WENO-Z+3）基础上，构造不同形式的全局光滑因子，提出一种改进的WENO-Z+3格式（NWENO-Z+3）.选取Sod激波管、双爆轰波碰撞、激波与熵波相互作用、双马赫反射等经典算例，考察该格式的计算性能，结果表明：NWENO-Z+3格式具有更低耗散性和更高的分辨率.数值研究柱形高压气体爆炸波在单舱室和连通舱室内部的传播过程及波系演化.结果表明：改进格式NWENO-Z+3能够较好地模拟包含高压比、高密度比的爆炸波系结构.

关键词: 三阶WENO格式, 全局光滑因子, 低耗散, 高分辨率, 爆炸波

Abstract: To improve dissipation characteristic and resolution for flow features of classical third-order WENO scheme (WENO-JS3). An improved third-order WENO-Z+ scheme (NWENO-Z+3) was constructed with a different global smoothness indicator. Several classical one-dimensional Riemann problems and double Mach reflection case were simulated to investigate computing performance of NWENO-Z+3 scheme. It indicated that NWENO-Z+3 scheme have better characteristics than schemes such as WENO-JS3, WENO-Z and WENO-Z+3 scheme with low numerical dissipation and high resolution to flow features. NWENO-Z+3 scheme was also used to investigate propagation and wave evolution of blast waves generated by cylindrical high pressure gas in single cabin and connected cabins. It indicated that NWENO-Z+3 scheme was suitable for simulating evolution of blast waves, which contains high pressure ratio and high density ratio.

Key words: third-order WENO scheme, global smoothness indicator, low dissipation, high resolution, blast waves

中图分类号:

V221.3

徐维铮, 孔祥韶, 吴卫国. 改进的三阶WENO-Z+格式及其应用[J]. 计算物理, 2018, 35(1): 13-21.

XU Weizheng, KONG Xiangshao, WU Weiguo. An Improved Third-order WENO-Z+3 Scheme and Its Application[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(1): 13-21.

参考文献

[1] MIURA A,MIZUKAKI T,SHIRAISHI T,et al.Spread behavior of explosion in closed space[J].Journal of Loss Prevention in the Process Industries,2002,12(1):231-237.
[2] RIGAS F,SKLAVOUNOS S.Experimentally validated 3-D simulation of shock waves generated by dense explosives in confined complex geometries[J].Journal of Hazardous Materials,2005,121(1-3):23-30.
[3] BENSELAMA A M,WILLIAM-LOUIS J P,MONNOYER F.A 1D-3D mixed method for the numerical simulation of blast waves in confined geometries[J].Journal of Computational Physics,2009,228(18):6796-6810.
[4] 高轩能,王书鹏,江媛.爆炸荷载下大空间结构的冲击波压力场分布及泄爆措施研究[J].工程力学,2010,27(4):226-233.
[5] 曲树盛,李忠献.地铁车站内爆炸波的传播规律与超压荷载[J].工程力学,2010,27(9):240-247.
[6] LIU X D,OSHER S,CHAN T.Weighted essentially non-oscillatory schemes[J].Journal of Computational Physics,1994,115(1):200-212.
[7] HARTEN A,ENGQUIST B,OSHER S,CHAKRAVARTHY S R.Uniformly high order accurate essentially non-oscillatory schemes, Ⅲ[J].Journal of Computational Physics,1987,71(2):231-303.
[8] JIANG G S,SHU C W.Efficient implementation of weighted ENO schemes[J].Journal of Computational Physics,1996,126(1):202-202.
[9] SHU C W. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws[M]. Springer Berlin Heidelberg,1998:325-432.
[10] SHU C W.High order weighted essentially nonoscillatory schemes for convection dominated problems[J].Siam Review,2009,51(1):82-126.
[11] 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.
[12] BORGES R,CARMONA M,COSTA B,DON W S.An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws[J].Journal of Computational Physics,2008,227(6):3191-3211.
[13] ACKER F,BORGES R B D R,COSTA B.An improved WENO-Z scheme[J].Journal of Computational Physics,2016,313:726-753.
[14] YAMALEEV N K,CARPENTER M H.Third-order energy stable WENO scheme[J].Journal of Computational Physics,2009,228(8):3025-3047.
[15] WU X,LIANG J,ZHAO Y.A new smoothness indicator for third-order WENO scheme[J].International Journal for Numerical Methods in Fluids,2015,81(7):451-459.
[16] 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.
[17] HU X Y,WANG Q,ADAMS N A.An adaptive central-upwind weighted essentially non-oscillatory scheme[J].Journal of Computational Physics,2010,229(23):8952-8965.
[18] KIM D,KWON J H.A high-order accurate hybrid scheme using a central flux scheme and a WENO scheme for compressible flowfield analysis[J].Journal of Computational Physics,2005,210(2):554-583.
[19] DON W S,BORGES R.Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes[J].Journal of Computational Physics,2013,250(4):347-372.
[20] 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.
[21] 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.
[22] SHI J,ZHANG Y T,SHU C W.Resolution of high order WENO schemes for complicated flow structures[J].Journal of Computational Physics,2003,186(2):690-696.
[23] 武从海,赵宁,田琳琳.一种改进的紧致WENO混合格式[J].空气动力学学报,2013,31(4):477-481.
[24] 吴晓帅,赵玉新. 低耗散中心-WENO混合格式[C]. 中国计算力学大会2014暨钱令希计算力学奖颁奖大会, 2014.
[25] 王来,吴颂平.无自由参数型混合格式[J].北京航空航天大学学报,2015,(2):318-322.
[26] QUIRK J J,KARNI S.On the dynamics of a shock-bubble interaction[J].J Fluid Mech, 1996,318(2):129-163.

改进的三阶WENO-Z+格式及其应用

An Improved Third-order WENO-Z+3 Scheme and Its Application

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 14

编辑推荐

Metrics

作者中心

审稿中心

期刊浏览

期刊介绍

[1]	沈亚玲, 封建湖, 郑素佩, 李雅蓉. 一种基于新型斜率限制器的理想磁流体方程的高分辨率熵相容格式[J]. 计算物理, 2022, 39(3): 297-308.
[2]	艾邦成, 张亮, 陈智. 低耗散非结构网格多维限制器[J]. 计算物理, 2018, 35(5): 545-553.
[3]	任炯, 封建湖, 刘友琼, 梁楠. 求解双曲守恒律方程的高分辨率熵相容格式[J]. 计算物理, 2014, 31(5): 539-551.
[4]	罗力, 封建湖, 唐小娟, 向量. 求解双曲守恒律方程的高分辨率熵稳定格式[J]. 计算物理, 2010, 27(5): 671-678.
[5]	邓树升, 耿继辉, 叶经方, 谭俊杰. 含运动变形物体流场的数值模拟[J]. 计算物理, 2009, 26(2): 200-210.
[6]	李宏. 高分辨率间断有限元方法[J]. 计算物理, 2004, 21(4): 367-376.
[7]	陈艺冰, 林忠. 多介质流体力学计算的守恒型高分辨率格式[J]. 计算物理, 2004, 21(2): 99-105.
[8]	张镭, 袁礼. 用改进的耦合型Level Set方法计算一维双介质可压缩流动[J]. 计算物理, 2001, 18(6): 511-516.
[9]	汪继文, 刘儒勋. 间断解问题的有限体积法[J]. 计算物理, 2001, 18(2): 97-105.
[10]	丁建中. MUSCL格式TV性质的非线性分析[J]. 计算物理, 1997, 14(6): 782-786.
[11]	李德元, 水鸿寿, 董素琴, 冯小四. 多介质流体力学计算的高分辨率格式[J]. 计算物理, 1996, 13(1): 57-64.
[12]	金保侠. 一种具有高分辨率特性的人工粘性法[J]. 计算物理, 1993, 10(2): 232-238.
[13]	种连荣, 黄敦. 塑料导爆管的数值计算(Ⅰ)[J]. 计算物理, 1992, 9(4): 376-376.
[14]	王保国, 卞荫贵. 求解三维欧拉流的隐-显式格式/及改进的三维LU算法[J]. 计算物理, 1992, 9(4): 423-425.