TITLE:
About One Discrete Mathematical Model of Perfect Fluid
AUTHORS:
Konstantin Eduardovich Plokhotnikov
KEYWORDS:
Perfect Fluid, Discrete Model, Liquid Particle, Branch Point, Turbulence, Interaction in the Cluster, The Laws of Conservation, Stochastic and Deterministic Components of the Flow, Computational Experiment, The Separation of Particles, The Effect of the Fermi-Pasta-Ulam, Calibration of Particle Velocities
JOURNAL NAME:
Open Journal of Modelling and Simulation,
Vol.4 No.3,
July
29,
2016
ABSTRACT: 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.