Numerical Models of Nonlinear Acoustic Wave Propagation in Medical Ultrasound Problems and Certain Applications of Aeroacoustics and Underwater Acoustics

The paper presents a review of numerical algorithms developed at the Laboratory of Medical and Industrial Ultrasound at Lomonosov Moscow State University, which are used to solve the evolution equations of nonlinear acoustics, such as the Burgers equation, the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, and the one-way Westervelt equation. The main results obtained using these numerical models in studying the propagation of intense acoustic waves in various media are presented. In particular, examples of solving problems in medical ultrasound, nonlinear aeroacoustics, and nonlinear underwater acoustics are considered. The generalization of one-way models to account for medium inhomogeneities is discussed, employing wide-angle parabolic approximation methods in three-dimensional problems.