Phase-error analysis of high-order finite difference time domain scheme and its influence on calculation results of impulse response in closed sound field
Phase-error analysis of high-order finite difference time domain scheme and its influence on calculation results of impulse response in closed sound field
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DOI：
10.1250/ast.28.295
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发表时间：
2007-09
影响因子：
0.7
通讯作者：
S. Sakamoto
中科院分区：
文献类型：
--
作者：
S. Sakamoto
为了通过数值分析获得声场中精确的脉冲响应，基于简单的泰勒展开，提出了一种高阶时域有限差分（FDTD）方法。用Von Neumann和Richtmyer色散分析方法对FDTD方法的精度进行了评价。结果发现，从传统的FDTD算法得到的不可避免的相位误差减少使用高阶计划与8个或更多的参考点。当在本研究中使用的方案中使用更高阶时，时间分辨率应该较小以减小相位误差。为了验证FDTD法计算封闭声场中脉冲响应的有效性，将数值结果与分离变量法得到的解析解进行了比较。结果发现，低阶FDTD的相位误差出现的波动的到达脉冲和波动可以减少使用高阶计划与一个小的时间分辨率。在对室内声学或室外噪声传播进行声场分析时，我们应该考虑的大规模声场或长时间计算的FDTD计算的精度受到相位误差的强烈影响，因此在进行此类数值分析时应该考虑该误差。
To obtain accurate impulse responses in a sound field by numerical analysis, a high-order finite difference time domain (FDTD) method was formulated on the basis of a simple Taylor expansion. The accuracy of the FDTD scheme was evaluated by Von Neumann and Richtmyer dispersion analysis. It was found that the unavoidable phase error obtained from the conventional FDTD algorithm is reduced using the high-order scheme with 8 or more reference points. When using higher orders in the scheme used in this study, the time resolution should be small to reduce the phase error. To validate the FDTD scheme for calculating the impulse response in a closed sound field, the numerical result was compared with an analytical solution obtained by the separation of variables method. It was found that the phase error for a low-order FDTD appeared as fluctuations of the arriving pulses and that the fluctuations can be reduced using the high-order scheme with a small time resolution. The accuracy of the FDTD calculation for a large-scale sound field or a long-time calculation, which we should consider when making a sound field analysis of room acoustics or outdoor noise propagation, is strongly influenced by the phase error and therefore the error should be considered when performing such numerical analyses.