A k-space method for moderately nonlinear wave propagation.
A k-space method for moderately nonlinear wave propagation.
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DOI：
10.1109/tuffc.2012.2372
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发表时间：
2012-08
期刊：
影响因子：
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通讯作者：
Clement GT
中科院分区：
文献类型：
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作者：
Jing Y;Wang T;Clement GT
提出了一种中等非线性波在吸收介质中传播的k空间方法。首先通过傅里叶变换将韦斯特丙酮方程转换到k空间，并通过修改的波矢时域格式求解。本方法不限于前向传播或抛物线近似。通过与解析解和时域有限差分法（FDTD）的比较，验证了该方法的有效性。结果发现，在均匀介质中获得准确的结果，网格的大小可以小到每波长两个点，和一个适度的非线性问题，柯朗-弗里德里希-路易数可以大到0.4。通过与传统的FDTD方法的比较，非线性波传播的k-空间方法在这里被示出是计算上更有效和更准确。k空间方法，然后研究三维非线性波传播通过颅骨，这表明，一个相对准确的聚焦可以实现在大脑中的高频率发送一个低频率的换能器。最后，使用单个图形处理单元实现k空间方法表明，它需要单核CPU计算的大约七分之一的计算时间。
A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant–Friedrichs–Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation.