### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 4pPAa7. Modification of the spectral method for describing nonlinear
acoustic waves containing shocks.

**Vera A. Khokhlova
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Oleg A. Sapozhnikov
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*Dept. of Acoust., Phys. Faculty, Moscow State Univ., Moscow 119899,
Russia
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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.]