Cite this article as:

Liverovskiy D. I., Shevirev S. P. Simulation of Incompressible Nonviscoussevere Fluid on a Regular Grid in Three-dimensional Space . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 3, pp. 335-340. DOI: https://doi.org/10.18500/1816-9791-2014-14-3-335-340

Language: 
Russian
Heading: 
Mechanics
UDC: 
533.6.011

Simulation of Incompressible Nonviscoussevere Fluid on a Regular Grid in Three-dimensional Space

Authors: 
Liverovskiy Dmitrii Igorevich, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , LiverovskiyDI@gmail.com
Shevirev Sergey Pavlovich, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , shevsp@rambler.ru
Abstract: 

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.

Key words: 
Davydov's method, fluid flow, method of large particles, free surface, Poisson equation for the pressure, the criterion of stability of difference schemes, symmetric flows.
DOI: 
https://doi.org/10.18500/1816-9791-2014-14-3-335-340
References
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2. Liverovskiy D. I., Shevirev S. P. Metod Davydova dlia sluchaia neszhimaemoi neviazkoi tiazheloi zhidkosti na reguliarnoi setke [Davydov’s method for a case of incompressible nonviscous heavy liquid on a regular grid]. Matematika. Mekhanika: sb. nauch. trudov, Saratov, Saratov Univ. Press, 2011, iss. 13, pp. 161–164 (in Russian).
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4. Shevirev S. P. Issledovanie dvumernoi skhemy metoda krupnykh chastits na ustoichivost’ [Research of the twodimensional scheme of a method of large particles on stability]. Differentsial’nye uravneniia i teoriia funktsii v prilozhenii k aerodinamike i teorii veroiatnostei: mezhvuz. nauch. sb. [Differential equations and the theory of functions in the Annex to aerodynamics and the theory of probability: a collection of papers]. Saratov, Saratov Univ. Press, 1987, iss. 7, pp. 16–21 (in Russian). 
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