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本文采用一维模型分析了时域离散化后有限元离散网格中波动的基本特征。文中讨论了时域离散化对波动的频散、截止频率及寄生振荡的影响,分析了由时域离散化引起的在频率域及由空间离散化引起的在波数域波动解的多重分支现象,并指出在研究中应取其基本分支。文中也给出了考虑时间步长影响的有限元离散化准则。研究结果表明,从模拟连续模型的精度上看,时域离散化使集中质最有限元法优于一致质量法,前者可取较大时间步长。从计算精度、容易程度及经济性各方面衡量,集中质量法均比一致质量法可取。本文的工作不但对波动有限元模拟的参数选取有指导意义,同时也是分析时域人工边界稳定性的基础工作之一。
In this paper, the one-dimensional model is used to analyze the basic characteristics of the wave in the finite element discrete grid after time domain discretization. In this paper, the effects of time domain discretization on the dispersion, cutoff frequency, and parasitic oscillations of the wave are discussed. The multi-branching phenomenon of wave solutions in the frequency domain and caused by spatial discretization caused by the time domain discretization is analyzed. And pointed out that the basic branch should be taken in the study. The finite element discretization criterion considering the influence of time step is also given in the paper. The research results show that, from the accuracy of the simulation continuous model, the time domain discretization makes the most finite element method of concentrating quality superior to the uniform quality method, and the former can take larger time steps. In terms of accuracy, ease of use, and economic efficiency, the centralized quality method is better than the uniform quality method. The work of this paper not only has guiding significance for the selection of the parameters of the fluctuating finite element simulation, but also is one of the basic tasks for the analysis of the stability of the temporal artificial boundary.