Geodesic
Numerical simulation of radially converging shock waves in the cavity of~a~bubble
Matematičeskoe modelirovanie, Tome 26 (2014) no. 4, pp. 3-20

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A numerical technique of investigating of the final stage of focusing of radially converging non-spherical shock wave in the neighborhood of the center of an axially symmetric cavitation bubble subjected to strong compression is presented. In the hydrodynamic model used compressibility of the liquid, heat conductivity of the vapor and liquid, evaporation and condensation on the interphase surface are taken into account, realistic wide-range equations of state are utilized. Moving meshes with explicit tracing of the bubble surface are applied. The technique is based on the TVD-modification of the Godunov scheme of the second order of accuracy in space and time. Its efficiency is gained due to allowing for the features of the problem in the final stage of focusing of the non-spherical shock wave in the central area of the bubble. After the value of deformation of the shock wave becomes greater than some threshold (i.e., when the shock wave becomes largely non-spherical) the curvilinear radially diverging mesh in the central area of the bubble is changed by the rectilinear oblique-angled mesh close to the Cartesian one. At the same moment the non-moving system of spherical co-ordinates is replaced by the cylindrical ones. Computation of parameters of cells from one mesh to the other is performed by a method of conservative interpolation. Some results of computation of a test problem and an example illustrating the working capacity of the presented approach are given.
Keywords: bubble collapse, strong compression of the bubble, radial convergence of shock waves. 
@article{MM_2014_26_4_a0,
     author = {A. A. Aganin and T. F. Khalitova and N. A. Khismatullina},
     title = {Numerical simulation of radially converging shock waves in the cavity of~a~bubble},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--20},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2014_26_4_a0/}
}
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A. A. Aganin; T. F. Khalitova; N. A. Khismatullina. Numerical simulation of radially converging shock waves in the cavity of~a~bubble. Matematičeskoe modelirovanie, Tome 26 (2014) no. 4, pp. 3-20. http://geodesic.mathdoc.fr/item/MM_2014_26_4_a0/