Godunov-type computation schemes are applied to numerical simulations of wave propagations in time-dependent heterogeneous media (solids and liquids). The parametric phase conjugation of a wide band ultrasound pulse is considered. The supercritical dynamics of the acoustic field is described for one-dimensional systems containing a parametrically active solid. The impulse response function, numerically calculated for a finite active zone in an infinite 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 for parametric excitations in an active zone of a solid layer, loaded by a semi-infinite liquid on one side and free on the other.

1.
B. Ya. Zel’dovich, N. F. Pilipetskii, and V. V. Shkumov, Principles of Phase Conjugation (Springer, Berlin, 1985).
2.
F. V.
Bunkin
,
D. V.
Vlasov
, and
Yu. A.
Kravtsov
, “
On problem of sound wave phase conjugation with amplification of conjugate wave
,”
Sov. J. Quantum Electron.
11
,
687
688
(
1981
).
3.
F. V.
Bunkin
et al., “
Wave phase conjugation of sound in water with bubbles
,”
Sov. Phys. Acoust.
29
,
169
171
(
1983
).
4.
R. B.
Thomson
and
C. E.
Quate
, “
Nonlinear interaction of microwave electric fields and sound in LiNbO3
,”
J. Appl. Phys.
42
,
907
919
(
1971
).
5.
M.
Ohno
and
K.
Takagi
, “
Enhancement of the acoustic phase conjugate reflectivity in nonlinear piezoelectric ceramics by applying static electric or static stress fields
,”
Appl. Phys. Lett.
69
,
3483
3485
(
1996
).
6.
A. P.
Brysev
,
L. M.
Krutyianskii
, and
V. L.
Preobrazhenskii
, “
Wave phase conjugation of ultrasonic beams
,”
Phys. Usp.
41
,
793
805
(
1998
), Reviews of topical problems.
7.
A. A.
Chaban
, “
On one nonlinear effect in piezoelectric semiconductors
,”
Sov. Phys. Solid State
9
,
3334
3335
(
1967
).
8.
D. L.
Bobroff
and
H. A.
Haus
, “
Impulse response of active coupled wave systems
,”
J. Appl. Phys.
38
,
390
403
(
1967
).
9.
M.
Fink
, “
Time reversal of ultrasonic fields
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
39
,
555
592
(
1996
).
10.
S. K.
Godunov
, “
A finite difference method for numerical computation of discontinuous solutions of the systems of the equations of fluid dynamics
,”
Mat. Sb.
47
,
357
393
(
1959
).
11.
E. F.
Toro
, “
The weighted average flux method applied to the Euler equations
,”
Philos. Trans. R. Soc. London, Ser. A
341
,
499
530
(
1992
).
12.
V. L. Preobrazhensky and P. Pernod, “Compression and decompression of ultrasonic echoes by means of parametric wave phase conjugation,” Proceedings of the 1998 IEEE Ultrasonic Symposium, Sendaı̈, Japan, 1998, Vol. 1, p. 889–891.
13.
B.
Van Leer
, “
Towards the ultimate conservative difference scheme V. A second order sequel to Godunov’s methods
,”
J. Comput. Phys.
32
,
101
136
(
1979
).
14.
P.
Roe
, “
Some contributions to the modeling of discontinuous flows,” Proceedings of the 15th AMS-SIAM Summer Seminar on Applied Mechanics
,
Lect. Appl. Math. SIAM
22
,
169
193
(
1985
).
15.
A. P.
Brysev
,
F. V.
Bunkin
,
M. F.
Hamilton
,
L. M.
Krutyianskii
,
K. B.
Cunningham
,
V. L.
Preobrazhensky
,
Yu. V.
Pyl’nov
,
A. D.
Stakhovskii
, and
S. J.
Younghouse
, “
Nonlinear propagation of quasi-plane conjugate ultrasonic beam
,”
Acoust. Phys.
44
,
641
650
(
1998
).
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