Godunov-type computation schemes are applied to numerical simulations of wa
ve propagations in time-dependent heterogeneous media (solids and liquids).
The parametric phase conjugation of a wide band ultrasound pulse is consid
ered. The supercritical dynamics of the acoustic field is described fur one
-dimensional systems containing a parametrically active solid. The impulse
response function, numerically calculated for a finite active zone in an in
finite medium above the threshold of absolute parametric instability, is in
a good agreement with the analytical asymptotic theory. The supercritical
evolution of the acoustic field spatial distribution is studied in detail f
or parametric excitations in an active zone of a solid layer, loaded by a s
emi-infinite liquid on one side and free on the other. (C) 2001 Acoustical
Society of America. [DOI: 10.1121/1.1328794].