[1]夏博阳,邵卫东,李军.三维间断伽辽金玻尔兹曼方法的完全匹配层吸收边界条件研究[J].西安交通大学学报,2020,54(07):113-120.[doi:10.7652/xjtuxb202007014]
 XIA Boyang,SHAO Weidong,LI Jun.Study on the Perfectly Matched Layer Absorbing Boundary Conditions for Three-Dimensional Discontinuous Galerkin Boltzmann Method[J].Journal of Xi'an Jiaotong University,2020,54(07):113-120.[doi:10.7652/xjtuxb202007014]
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三维间断伽辽金玻尔兹曼方法的完全匹配层吸收边界条件研究
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《西安交通大学学报》[ISSN:0253-987X/CN:61-1069/T]

卷:
54
期数:
2020年第07期
页码:
113-120
栏目:
出版日期:
2020-07-08

文章信息/Info

Title:
Study on the Perfectly Matched Layer Absorbing Boundary Conditions for Three-Dimensional Discontinuous Galerkin Boltzmann Method
文章编号:
0253-987X(2020)07-0113-08
作者:
夏博阳1 邵卫东2 李军1
1.西安交通大学能源与动力工程学院, 710049, 西安; 2.中国航发商用航空发动机有限责任公司, 200241, 上海
Author(s):
XIA Boyang1 SHAO Weidong2 LI Jun1
1. School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China; 2. AECC Commercial Aircraft Engine Co. Ltd., Shanghai 200241, China
关键词:
完全匹配层 间断伽辽金玻尔兹曼方法 吸收边界条件 计算气动声学
Keywords:
perfectly matched layer discontinuous Galerkin Boltzmann method absorbing boundary condition computational aeroacoustics
分类号:
V211.3
DOI:
10.7652/xjtuxb202007014
文献标志码:
A
摘要:
为解决计算气动声学数值模拟中远场边界反射问题,在三维间断伽辽金有限元玻尔兹曼方法框架下应用完全匹配层算法构造了吸收边界条件,并采用了两种不同的离散求解公式。利用三维高斯脉动源数值案例测试了两种公式的有效性和稳定性,发现仅有一种公式既能有效衰减反射波又具有良好的稳定性; 接着研究了影响完全匹配层算法无反射性能的若干因素,其中无反射性能采用归一化误差范数来衡量。研究表明:衰减因子总是存在最优值,且最优值仅与吸收层的参数有关,而与高斯脉动源自身参数无关,故所定义的归一化误差范数具有一定的普适性; 当衰减因子采用幂函数分布律时,幂指数取2时无反射性能更好,取4时无反射性能随衰减因子变化更平缓; 吸收层厚度和区域半径越大,无反射性能越好,但相应的计算量也显著提高。研究工作可为构造更加实用有效的无反射边界条件提供参考。
Abstract:
To solve the problem of far-field boundary reflection in aeroacoustic simulation, the perfectly matched layer(PML)technique is introduced into the three-dimensional discontinuous Galerkin Boltzmann method to construct absorbing boundary conditions using two different discretized formulas. Both formulas are tested in three-dimensional Gaussian pulse cases to confirm their stability and effectiveness. It shows that only one formula can both effectively dampen the reflecting waves and preserve excellent stability. Several factors which affect the non-reflecting performance of PML are studied and the performance is measured by newly defined normalized norms. The results show that the damping coefficient has an optimal value which is related to the parameters of the PML rather than the parameters of Gaussian pulses, indicating that the normalized norms are of universality to some extent. If the damping coefficient is in a power-law distribution, then using exponent of 2 can reach better non-reflecting performance, while using exponent of 4 leads to a more gradual performance change with respect to damping coefficient. A thicker absorbing layer and a larger domain can improve the non-reflecting performance but increase the amount of computation. This work can serve as a reference for constructing more effective and practical non-reflecting boundary conditions.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2019-12-26。作者简介: 夏博阳(1996—),男,硕士生; 李军(通信作者),男,教授,博士生导师。
更新日期/Last Update: 2020-07-10