The general equations of finite amplitude acoustics, including classical absorption effects and second-order nonlinear effects, are written in a form suitable for two-dimensional numerical solution. A finite difference scheme then is applied to numerically solve the equations. To demonstrate the method, examples are given of spherical free-field propagation, normal plane reflection from a hard surface, and oblique spherical reflection from a hard surface for spark pulses. This method has an advantage over Burgers’ equation methods, one-way wave equation methods, and Pestorius type algorithms in that it can predict the interaction of multiple finite amplitude acoustic waves at arbitrary propagation angles.
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Sparrow et al. (1991) studied this question.