ИСТИНА

Numerical simulations of intense sound fields are employed in research involving therapeutic ultrasound, underwater acoustics, and air acoustics. Nonlinear evolution equations such as the Burgers and Khokhlov-Zabolotskaya-Kuznetsov equations generalized for biological tissue and relaxing media, and the one-way Westervelt equation, have been used for simulating strongly nonlinear sound fields with shocks. Marching schemes based on operator splitting enable modeling of different wave phenomena, e.g., nonlinearity, diffraction, attenuation, and dispersion, using the most effective algorithm for each effect. Simulation of strong nonlinear propagation effects leading to formation of steep shocks has been a challenging problem. Time-domain modeling has proven to be most effective because the number of operations over each propagation step is proportional to the number of grid points in the time window, whereas frequency-domain schemes require the number of harmonics squared. This talk will describe and compare specific features, accuracy, and effectiveness of various time-domain algorithms that have been developed over the years to simulate nonlinear effects in shock-wave propagation regimes. Algorithms based on the exact solution of the lossless Burgers equation with an interpolation procedure, an intrinsic coordinates algorithm, conventional conservative finite-difference schemes, and the Godunov-type shock-capturing method will be discussed. [Work partially supported by RSF №25-12-00157.]