Geodesic
Spatial modeling of water foam dynamics with moving Lagrangian grids under shock wave impact
Numerical methods and programming, Tome 15 (2014) no. 3, pp. 427-440.

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The dynamic processes of wave pulse propagation in an aqueous foam and the air shock wave interaction with the foam barrier are numerically modeled and studied. The proposed method of solution is based on a two-phase gas-liquid mixture model using a wide-range state equation for describing the thermodynamic properties of mixture components. The shock-capturing method with moving Lagrangian grids is used, which allows one to simplify the numerical analysis of two-phase shock-wave flows. The two-dimensional axisymmetric model is verified by comparison with the numerical results obtained on the basis of the spherically symmetric one-dimensional model. The flow regimes causing the air shock wave blocking by foam barriers, followed by the formation of vortex structures, are analyzed. The efficiency and features of foam damping properties are discussed.
Keywords: pressure pulse, gas-liquid foam, two-phase model, spatial problems, numerical simulation, moving Lagrangian grids, two-phase wave flows. 
@article{VMP_2014_15_3_a5,
     author = {R. Kh. Bolotnova and U. O. Agisheva},
     title = {Spatial modeling of water foam dynamics with moving {Lagrangian} grids under shock wave impact},
     journal = {Numerical methods and programming},
     pages = {427--440},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2014_15_3_a5/}
}
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R. Kh. Bolotnova; U. O. Agisheva. Spatial modeling of water foam dynamics with moving Lagrangian grids under shock wave impact. Numerical methods and programming, Tome 15 (2014) no. 3, pp. 427-440. http://geodesic.mathdoc.fr/item/VMP_2014_15_3_a5/