Causal impulse response for circular sources in viscous media.
Causal impulse response for circular sources in viscous media.
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DOI：
10.1121/1.2885737
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发表时间：
2008-04
期刊：
影响因子：
--
通讯作者：
J. Kelly;R. McGough
中科院分区：
文献类型：
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作者：
J. Kelly;R. McGough
推导了斯托克斯波动方程中速度势的因果脉冲响应，用于计算粘性介质中圆形活塞产生的瞬态速度势场。利用材料脉冲响应函数法对因果格林函数进行了数值验证。然后，利用先前为快速近场方法导出的表达式，计算了折板圆形活塞在近场和远场区域内的因果、有损脉冲响应。用有损失的因果脉冲响应计算了粘性介质中的瞬态速度势场，并与无损失脉冲响应计算结果进行了比较。定量分析了计算速度势场的数值误差在一定范围内的粘性松弛时间和活塞半径。结果表明，在活塞端面附近和较大的松弛时间产生的误差最大，其他位置的误差相对较小。与以往需要数值傅里叶反变换来评估有损脉冲响应的频域方法不同，本方法直接在时域中计算有损脉冲响应。结果表明，这种因果脉冲响应对于同时考虑粘性介质中衍射和二次频率相关衰减的时域计算是理想的。
The causal impulse response of the velocity potential for the Stokes wave equation is derived for calculations of transient velocity potential fields generated by circular pistons in viscous media. The causal Green's function is numerically verified using the material impulse response function approach. The causal, lossy impulse response for a baffled circular piston is then calculated within the near field and the far field regions using expressions previously derived for the fast near field method. Transient velocity potential fields in viscous media are computed with the causal, lossy impulse response and compared to results obtained with the lossless impulse response. The numerical error in the computed velocity potential field is quantitatively analyzed for a range of viscous relaxation times and piston radii. Results show that the largest errors are generated in locations near the piston face and for large relaxation times, and errors are relatively small otherwise. Unlike previous frequency-domain methods that require numerical inverse Fourier transforms for the evaluation of the lossy impulse response, the present approach calculates the lossy impulse response directly in the time domain. The results indicate that this causal impulse response is ideal for time-domain calculations that simultaneously account for diffraction and quadratic frequency-dependent attenuation in viscous media.