Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

Akademgorodok, Novosibirsk, Russia, June 24 - 29, 2001

Abstracts

Novosibirsk participants

The propagation of concentration waves in a bubbly fluid

Chesnokov A.

Lavrentyev Institute of Hydrodynamics (Novosibirsk)

The kinetic model of rarefied bubbly flow derived by G. Russo and P. Smereka [1] is considered. New exact solutions of 1-dimensional non-linear integrodifferentional equation are found. The solution of the problem on propagation small perturbations is given. Also we obtain and analyse dispersion relation for 3-dimensional Russo-Smereka kinetic equations.

The construction of exact solution based on conservation laws and general symmetries [2]. Self-similar solutions that describe penetration of bubbles into the unperturbed region through which the simple wave propagates have been obtained (flows of bubbly fluid with critical layer). Solution of linearized kinetic equation based on transformation to characteristic form and inverse singular integral equation. In 3-dimension case the rate of small disturbance propagation in bubbly flow is determined.

References

1. Russo G., Smereka P. Kinetic theory for bubbly flow I: collisionless case // SIAM J. Appl. Math. 1996. V.56, N 2. P. 327-357.

2. Teshukov V.M. Characteristics, conservation laws and symmetries of the kinetic equations for motion of bubbles in a fluid // Prikl. Mech. Tech. Fiz., 40, N 2, 86-100 (1999).

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Note. Abstracts are published in author's edition

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