Monte Carlo solutions of a joint PDF equation for turbulent flows in general orthogonal coordinates

The modeled transport equation for the joint probability density function (pdf) of the velocities and a single scalar composition in a turbulent flow is an integro-differential equation in up to seven independent variables and time. Because of its large dimensionality, this equation may be efficiently solved by a Monte Carlo method. An algorithm is developed that allows the pdf equation to be solved in a general orthogonal coordinate system. The method is based on a Lagrangian approach in which the behavior of fluid particles in a turbulent flow is modeled and particle trajectories are computed in the Monte Carlo solution algorithm. The technique is applied to three self-similar turbulent free shear flows: the plane mixing layer, the plane jet, and the axisymmetric jet. Numerical test results are presented which compare the new algorithm with earlier methods, verify the statistical error estimates, and demonstrate convergence.