APPLICATION OF GENERALIZED FINITE DIFFERENCE METHOD IN ACOUSTIC ANALYSIS OF CAVITY WITH IMPEDANCE BOUNDARY1)
Chen Zengtao*, Wang Fajie,*,†,2), Wang Chao**Power Integration and Energy Storage System Engineering Technology Center, Qingdao University. College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, Shandong, China †Institute of Multifunctional Materials and Structural Mechanics, Qingdao University, Qingdao 266071, Shandong, China
Abstract Acoustic analysis plays significant role in engineering calculations such as noise control and indoor sound insulation. Since the practical acoustic problems usually involve sound-absorbing materials, it is very necessary to analyze acoustic problems with impedance boundary conditions. The generalized finite difference method is a new mesh-less numerical discretization method, this method is based on Taylor series expansion of multivariate function and weighted least square, the partial derivatives of unknown values in the governing equation are expressed as a linear combination of function values at supporting nodes. In this paper, the generalized finite difference method is applied to the analysis of cavity acoustics with impedance boundary conditions firstly, and the corresponding numerical discrete scheme is established. Compared with traditional algorithms, the developed numerical model is a local meshless method with the merits of being mathematically simple, numerically accurate and easy to large-scale acoustic analysis. A benchmark numerical example with analytical solution is examined to verify the influence of the total number of nodes and the number of local supporting nodes on the numerical results, and to obtain an empirical formula of the relationship between maximum computable frequency and node spacing. In addition, the generalized finite difference method is applied to two-dimensional and three-dimensional complex acoustic models without analytical solutions, and is compared with the FEM solutions obtained by COMSOL Multiphysics. Numerical experiments demonstrate that the generalized finite difference method is an efficient, accurate, stable and convergent numerical method, and has broad application prospects in the acoustic analysis of cavities with impedance boundaries. Keywords:meshless method;generalized finite difference method;cavity acoustic problems;impedance boundary;finite element method
PDF (7341KB)元数据多维度评价相关文章导出EndNote|Ris|Bibtex收藏本文 本文引用格式 陈增涛, 王发杰, 王超. 广义有限差分法在含阻抗边界空腔声学分析中的应用1). 力学学报[J], 2021, 53(4): 1183-1195 DOI:10.6052/0459-1879-20-311 Chen Zengtao, Wang Fajie, Wang Chao. APPLICATION OF GENERALIZED FINITE DIFFERENCE METHOD IN ACOUSTIC ANALYSIS OF CAVITY WITH IMPEDANCE BOUNDARY1). Chinese Journal of Theoretical and Applied Mechanics[J], 2021, 53(4): 1183-1195 DOI:10.6052/0459-1879-20-311
Table 1 表1 表1总节点数$N=17 996$时, 不同支撑点数下的最大相对误差、均方根误差和计算时间(CT) Table 1When $N=17 996$, the $MRE$s, $RMSE$s and calculation time (CT) under different number of supporting nodes
Table 2 表2 表2局部支撑点数为$m=12$时, 不同总节点数下的最大相对误差、均方根误差和计算时间(CT) Table 2When $m=12$, the $MRE$s, $RMSE$s and calculation time (CT) under different number of total nodes
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