Computational Methods

Computational methods covered in this chapter apply primarily to finite-amplitude sound propagating in predominantly a single coordinate direction. Methods for solving the Burgers, KZK, and NPE equations in either the frequency or time domain are described. The combined effects of nonlinearity, absorption, dispersion, and diffraction in the model equations are taken into account by employing operator splitting. A frequency-domain algorithm is discussed that employs a spatial Fourier transform to account for diffraction without resorting to the parabolic approximation inherent in the KZK and NPE equations. A general time-domain algorithm is described that is not restricted to progressive waves.