Vera A. Khokhlova
Oleg A. Sapozhnikov
Dept. of Acoust., Phys. Faculty, Moscow State Univ., Moscow 119899, Russia
Numerical simulations of finite amplitude sound waves become particularly time consuming in the case of strongly distorted waveforms that contain shocks. To improve the efficiency of time domain numerical codes, weak shock theory can be used to separate the description of the shock fronts from the evolution of the continuous segments of the wave. The idea of the present work is to modify the spectral method by taking into account the known asymptotic behavior of high-frequency components in shock waves. Use of asymptotic results permits the number of spectral components retained in the numerical computations to be reduced. A finite set of coupled equations for the spectral amplitudes, which approximates the infinite set of spectral equations corresponding to an exact formulation, is obtained for the simple wave equation. This reduction is achieved by introducing asymptotic expressions for the high-frequency components in sawtoothlike waves. Several model problems are studied. It is shown that less than 15 harmonics require numerical calculation in order to obtain an adequate description of the evolution of an initially sinusoidal wave to a sawtoothlike waveform. [Work supported by ISF and the Russian Fund for Fundamental Investigations.]