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
1. Belotserkovskii O. M., Davydov Yu. M. Metod krupnykh chastits v gazovoi dinamike. Vychislitel’nyi eksperiment [Method of coarse particles in gas dynamics]. Moscow, Nauka, 1972, 392 p. (in Russian).
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).
3. Potter D. Computational Physics. New York, John Wiley and Sons, 1973.
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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