Geodesic
Simulating the dynamics of a fluid with a free surface in a gravitational field by a CABARET method
Matematičeskie zametki SVFU, Tome 29 (2022), pp. 77-94.

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An explicit conservative-characteristic CABARET method is proposed for calculating the dynamics of a fluid with a free surface in a gravitational eld in a weakly compressible approximation. The developed method has the second order of approximation in time and space, minimum computational template of one space-time cell and minimum numerical viscosity. A difference scheme is tested on problems with various values of the surface tension coefficient and gravitational acceleration with various signs,including the problem of the development of the Rayleigh-Taylor instability. Taking into account the forces of surface tension makes it possible to get rid of high-frequency oscillations on the free surface when calculating unstable problems and regularizes the solution.
Keywords: equations of hyperbolic type, balance-characteristic schemes, mixed Euler–Lagrangian variables, weakly compressible fluid, Rayleigh–Taylor instability
Mots-clés : surface tension. 
@article{SVFU_2022_29_a6,
     author = {N. A. Afanasiev and V. M. Goloviznin and P. A. Maiorov and A. V. Solov'ev},
     title = {Simulating the dynamics of a fluid with a free surface in a gravitational field by a {CABARET} method},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {77--94},
     publisher = {mathdoc},
     volume = {29},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2022_29_a6/}
}
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N. A. Afanasiev; V. M. Goloviznin; P. A. Maiorov; A. V. Solov'ev. Simulating the dynamics of a fluid with a free surface in a gravitational field by a CABARET method. Matematičeskie zametki SVFU, Tome 29 (2022), pp. 77-94. http://geodesic.mathdoc.fr/item/SVFU_2022_29_a6/