Geodesic
2D and 3D simulation of Rayleigh--Taylor instability in cylindrical and spherical geometries
Matematičeskoe modelirovanie, Tome 16 (2004) no. 2, pp. 69-86

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Numerical simulations for cylindrical and spherical geometries are presented, which study linear and nonlinear stages of evolution of small perturbations at the interface of two incompressible, non-viscous, nonheat-conducting liquids being under effect of Rayleigh–Taylor instability. Initial perturbations of the interface are considered for two cases: when the flow is described with two and three spatial variables. Results of the numerical simulations of the linear evolution stage for the small perturbations are in good agreement with the analytical laws of small single-mode perturbation evolution, derived in linearized formulation (basic solution is at rest) for cylindrical and spherical geometries. Effect of dimensionality of space and geometry (plane, cylindrical or spherical) on the evolution of perturbations is studied for nonlinear stage. Basic characteristics of the difference methods implemented in MAH and MAH-3 software packages used for numerical studies are briefly described. 
@article{MM_2004_16_2_a5,
     author = {N. N. Anuchina and V. I. Volkov and N. S. Eskov and O. S. Ilyutina and O. M. Kozyrev},
     title = {2D and {3D} simulation of {Rayleigh--Taylor} instability in cylindrical and spherical geometries},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {69--86},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_2_a5/}
}
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N. N. Anuchina; V. I. Volkov; N. S. Eskov; O. S. Ilyutina; O. M. Kozyrev. 2D and 3D simulation of Rayleigh--Taylor instability in cylindrical and spherical geometries. Matematičeskoe modelirovanie, Tome 16 (2004) no. 2, pp. 69-86. http://geodesic.mathdoc.fr/item/MM_2004_16_2_a5/