Geodesic
Simulation of Incompressible Nonviscoussevere Fluid on a Regular Grid in~Three-dimensional Space
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 335-340.

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This study focuses on modification of the method of Davydov (large particles) in the case of incompressible liquid. We consider the simulation of a heavy incompressible nonviscous fluid by Davydov's modified method in a three-dimensional case. Besides, comparison of the received results with a two-dimensional case is carried out. Formulas of modified Davydovs's method for the case of three spatial dimensions are lead out including difference analogue of the three-dimensional Poisson equation for the pressure. The criterion of stability is generalized. The description of the algorithm for constructing a three-dimensional free surface is provided. Implemented a three-dimensional computer graphics, showing development processes in online mode. 
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D. I. Liverovskiy; S. P. Shevirev. Simulation of Incompressible Nonviscoussevere Fluid on a Regular Grid in~Three-dimensional Space. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 335-340. http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a13/

[1] Belotserkovskii O. M., Davydov Yu. M., Method of coarse particles in gas dynamics, Nauka, M., 1972, 392 pp. (in Russian)

[2] Liverovskiy D. I., Shevirev S. P., “Davydov's method for a case of incompressible nonviscous heavy liquid on a regular grid”, sb. nauch. trudov, Matematika. Mekhanika, 13, Saratov Univ. Press, Saratov, 2011, 161–164 (in Russian)

[3] Potter D., Computational Physics, John Wiley and Sons, New York, 1973 | MR | Zbl

[4] Shevirev S. P., “Research of the two-dimensional scheme of a method of large particles on stability”, a collection of papers, Differential equations and the theory of functions in the Annex to aerodynamics and the theory of probability, 7, Saratov Univ. Press, Saratov, 1987, 16–21 (in Russian)