Stochastic parametric resonance of the elastic dumbbell in the viscous fluid
Authors: Schadinskiy D.M.  
Published in issue: #2(19)/2018  
DOI: 10.18698/2541800920182253  
Category: Mathematics  Chapter: Computational Mathematics 

Keywords: lowscale turbulence, particles oscillation, stochastic parametric resonance, Verlet algorithm, EulerMaruyama method 

Published: 30.01.2018 
The article analyses the occurrence of resonance in the system of two point particles bound with the elastic thread and dipped into the random field of the fluid velocity by means of the numerical simulation technique. The study shows that the considered system of two particles can be the simplest model of the polymeric thread in the turbulent flow. We bring out the dynamic equation system for the relative motion of the particles in the random field of the fluid velocity. The relative fluid velocity dependency on the interparticle distance is taken into account. We use an EulerMaruyama method for the numerical simulation of the stochastic processes. The dynamics of the relative motion of the particles with regard for the elastic constraint is calculated through the Verlet algorithm. The article analyses the order of the EulerMaruyama method convergence and the order of Verlet integration approximation. The work presents the results of testing the Verlet integration by means of the correlation with the exact solutions for oscillators at resonance in the viscous fluid. We numerically set limits for resonance excitation in the elastic dumbbell for the periodic and random field of the fluid velocity.
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