Geodesic
Modeling of wave processes in a~vapor-liquid medium
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 3, pp. 261-270

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Numerical methods for modeling nonlinear wave processes in a vapor-liquid medium for a model two-phase spherical symmetric cell, with an applied pressure jump on its external boundary are considered. The viscosity and compressibility of liquid are neglected as well as the space variation of vapor in the bubble. The problem is described by the heat equations in vapor and liquid, and by the system of ODEs for velocity, pressure and a radius at the bubble boundary. The space discretization of equations is made by an implicit finite-volume scheme on the dynamic adaptive grid with the geometrical refinement near the bubble boundary. The “nonlinear” iterations are implemented at each time step to provide a necessary high accuracy. The results of numerical experiments are presented and discussed for critical thermodynamic parameters of water, for different initial values of the bubble radius and pressure jumps. 
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     author = {V. G. Gasenko and G. V. Demidov and V. P. Il'in and I. A. Shmakov},
     title = {Modeling of wave processes in a~vapor-liquid medium},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {261--270},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_3_a2/}
}
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V. G. Gasenko; G. V. Demidov; V. P. Il'in; I. A. Shmakov. Modeling of wave processes in a~vapor-liquid medium. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 3, pp. 261-270. http://geodesic.mathdoc.fr/item/SJVM_2012_15_3_a2/