ANALYTICAL AND NUMERICAL SOLUTION OF THE EQUATION FOR THE PROBABILITY DENSITY FUNCTION OF THE PARTICLE VELOCITY IN A TURBULENT FLOW

A study has been made of the random motion of inertial particles in a homogeneous isotropic turbulent gas fl ow. Fluctuations of the gas velocity along the particle path were modeled by the Gaussian random process with a fi nite time of degeneracy of the autocorrelation function. A closed equation has been obtained for the probability density function of the particle velocity, for which two methods of numerical solution have been proposed: using the fi nitedifference scheme and using one based on direct numerical modeling of an empirical probability density function. The empirical probability density function was obtained as a result of the averaging of random particle paths, which are a solution of a system of ordinary stochastic differential equations. The results of numerical calculation have been compared with the analytical solution describing the dynamics of the probability density function of the particle-velocity distribution.
   
Author:  I. V. Derevich and A. K. Klochkov
Keywords:  probability density function, stochastic ordinary differential equation, two-phase turbulence, difference scheme, autocorrelation function, Green′s function, direct numerical modeling
Page:  1043