基于映射函数的三阶WENO改进格式及其应用

徐维铮; 孔祥韶; 吴卫国

doi:10.21656/1000-0887.370345

基于映射函数的三阶WENO改进格式及其应用

doi: 10.21656/1000-0887.370345

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

基金项目: 国防基础研究项目(B1420133057);国家自然科学基金(51409202)；中央高校基本科研业务费（2016-YB-016）

详细信息

作者简介:
徐维铮(1991—) ，男，博士生（E-mail: xuweizheng@whut.edu.cn）;孔祥韶(1983—) ，男，副教授，硕士生导师（通讯作者. E-mail: kongxs@whut.edu.cn）.

中图分类号: O346.1
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出版历程
- 收稿日期: 2016-11-14
- 修回日期: 2016-12-26
- 刊出日期: 2017-10-15

An Improved rd-Order WENO Scheme Based on Mapping Functions and Its Application

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

Funds: The National Natural Science Foundation of China(51409202)

摘要

摘要: 低耗散、高分辨率激波捕捉格式对含激波流场的数值模拟具有重要意义.在传统三阶WENO格式（WENO-JS3）和三阶WENOZ格式（WENO-Z3）基础上，基于映射函数，给出WENO-M3、WENOMZ3格式.选用Sod激波管、激波与熵波相互作用、双爆轰波碰撞及双Mach(马赫)反射等经典算例，考察上述格式的计算性能.数值结果表明，WENO-MZ3格式相较其他格式具有耗散低、对流场结构分辨率高的特性.为了进一步扩展WENO-MZ3格式的应用范围，采用该格式数值研究封闭方形舱室内柱形高压、高密度气体爆炸波传播过程，波系演化规律以及壁面典型测点压力载荷.数值计算结果表明WENO-MZ3格式能够较好地模拟包含高压比、高密度比的爆炸波且给出数值耗散较小的壁面压力载荷.
- 三阶WENO格式 /
- 映射函数 /
- 高分辨率 /
- 低耗散 /
- 爆炸
Abstract: Low-dissipation and high-resolution shock-capturing schemes are of great significance for numerical simulation of flow fields containing shock waves. The WENO-M3 and WENO-MZ3 schemes were proposed with mapping functions based on the classical 3rd-order WENO scheme (WENO-JS3) and the 3rd-order WENO-Z scheme (WENO-Z3). Several classical 1D Riemann problems and double Mach reflection cases were simulated with the above schemes. The simulation results indicate that the WENO-MZ3 scheme has better characteristics of low numerical dissipation and high resolution for the flow features among all the schemes. To expand the application scope of the WENO-MZ3 scheme, the propagation and evolution of blast waves generated by cylindrical high pressure gas in a closed square cabin were investigated. Moreover, 2 typical pressure gauging points on the walls were monitored during the simulation. It is indicated that the WENO-MZ3 scheme is suitable for simulating the evolution of blast waves containing high pressure ratios and high density ratios. The WENO-MZ3 scheme gives lower-dissipation results than the WENO-JS3 scheme for the pressure load on the walls.
- 3rd-order WENO scheme /
- mapping function /
- high resolution /
- low dissipation /
- explosion

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