Geodesic
Simulation of strong compression of a gas cavity in liquid
Matematičeskoe modelirovanie, Tome 20 (2008) no. 11, pp. 89-103.

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A technique of computation of strong compression of a gas cavity in liquid is presented. The shape of the cavity during compression is axially symmetric with relatively small deviation from the spherical one. The motion of the gas and liquid is described by two-dimensional dynamic equations of compressible liquid and gas with realistic equations of state. The influence of viscosity and heat conductivity is not taken into account. The cavity surface is defined as a contact boundary with the action of the surface tension. The coupled Euler–Lagrange coordinates with the bubble surface as a coordinate one are used. The spherical coordinates are taken as fixed ones. The equations of gas and liquid dynamics are solved by Godunov's method of the second-order of accuracy in space and time. The efficiency of the technique is investigated by computation of several model problems. It has been found that the technique proposed is more efficient than classic Godunov's scheme of the first order accuracy, which is usually used in literature for problems of strong compression of the bubble. One of possible scenarios of influence of small distortions of the spherical shape of the cavity on the distortion of sphericity of the radially-converging shock wave arising during strong compression has been shown. 
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A. A. Aganin; M. A. Il'gamov; T. F. Khalitova. Simulation of strong compression of a gas cavity in liquid. Matematičeskoe modelirovanie, Tome 20 (2008) no. 11, pp. 89-103. http://geodesic.mathdoc.fr/item/MM_2008_20_11_a7/

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