A Monte Carlo method for the PDF equations of turbulent flow

Abstract

A Monte Carlo method is presented which simulates the transport equations of joint probability density functions (pdf's) in turbulent flows. (Finite-difference solutions of the equations are impracticable, mainly because of the large dimensionality of the pdf's.) Attention is focused on an equation for the joint pdf of chemical and thermodynamic properties in turbulent reactive flows. It is shown that the Monte Carlo method provides a true simulation of this equation, and that the amount of computation required increases only linearly with the number of properties considered. Consequently, the method can be used to solve the pdf equation for turbulent flows involving many chemical species and complex reaction kinetics. Monte Carlo calculations of the pdf of temperature in a turbulent mixing layer are reported. These calculations are in good agreement with the measurements of Batt (1977).