Abstract
A k-space method for 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 Mast et al., IEEE Tran. Ultrason. Ferroelectr. Freq. Control 48,
341-354 (2001). 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 the finite element method. It is
found that, in order 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 small as 0.4.
As a result, the k-space method for nonlinear wave propagation is shown here to
be computationally more efficient than the conventional finite element method
or finite-difference time-domain method for the conditions studied here.
However, although the present method is highly accurate for weakly
inhomogeneous media, it is found to be less accurate for strongly inhomogeneous
media. A possible remedy to this limitation is discussed.
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