Geodesic
Numerical modeling of the solitary pressure wave propagation in a~liquid containing bubble area
Matematičeskoe modelirovanie, Tome 21 (2009) no. 3, pp. 3-17.

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The two-dimensional problem of a solitary pressure wave in a liquid with air bubbles is considered. The liquid is supposed to be compressible, dynamics of bubbles oscillation are described by Herring–Flynn equation. Conditions of regimes of the pressure wave propagation in the liquid with bubbles area of rectangular section are investigated. Influence of the gas volume content and of the channel width on a waveform is studied. Values of parameters of mathematical model for which the pressure wave amplitude surpasses initial one are obtained. The wave structure in bubble area is discussed. Parameters at which the stable mode is keeping for a long time in the bubble channel are found. 
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N. A. Kudryashov; N. A. Teterev. Numerical modeling of the solitary pressure wave propagation in a~liquid containing bubble area. Matematičeskoe modelirovanie, Tome 21 (2009) no. 3, pp. 3-17. http://geodesic.mathdoc.fr/item/MM_2009_21_3_a0/

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