Аннотация:In work, it is constructed a discrete mathematical model of motion of a perfect fluid. The fluid is
represented as an ensemble of identical so-called liquid particles, which are in the form of extended
geometrical objects: circles and spheres for two-dimensional and three-dimensional cases,
respectively. The mechanism of interaction between the liquid particles on a binary level and on
the level of the n-cluster is formulated. This mechanism has previously been found by the author
as part of the mathematical modeling of turbulent fluid motion. In the turbulence model was derived
and investigated the potential interaction of pairs of liquid particles, which contained a singularity
of the branch point. Exactly, this is possible to build in this article discrete stochastic-deterministic
model of an ideal fluid. The results of computational experiment to simulate
various kinds of flows in two-dimensional and three-dimensional ensembles of liquid particles are
presented. Modeling was carried out in the areas of quadratic or cubic form. On boundary of a region
satisfies the condition of elastic reflection liquid particles. The flows with spontaneous separation
of particles in a region, various kinds of eddy streams, with the quite unexpected statistical
properties of an ensemble of particles characteristic for the Fermi-Pasta-Ulam effect were found.
We build and study the flow in which the velocity of the particles is calibrated. It was possible using
the appropriate flows of liquid particles of the ensemble to demonstrate the possibility to reproduce
any prescribed image by manipulating the parameters of the interaction. Calculations of
the flows were performed with using MATLAB software package according to the algorithms presented
in this article.