Numerical modeling of ultrasound difference-frequency wave generation under conditions of shock front formation

The problem of generation and propagation of a difference-frequency wave formed as the interaction of two high-intensity high-frequency pump waves is considered and described by the nonlinear Burgers equation. It is known that the evaluation of the nonlinear operator in this equation is particularly difficult due to the necessity of retaining several thousands of spectral components, especially under conditions of shock front formation in the waveform. For this reason, the method which enables to reduce the number of spectral components in the numerical algorithm is considered. The only restriction is that it should not affect the accuracy of calculation of a difference-frequency wave. The above method is compared to an earlier proposed one for a set of harmonics retaining in the nonlinear numerical scheme. It is shown that the new method is more accurate at shorter distances, but it outmatches the previous one on large distances only when using a bigger number of spectral components retained in the algorithm. Such behaviour is explained by the retention of a smaller number of high-frequency and a larger number of combination components.