Probability density function/Monte Carlo simulation of near-wall turbulent flows

Probability density function (p.d.f.) methods are extended to include modelling of wall-bounded turbulent flows. A p.d.f. near-wall model is developed in which the generalized Langevin model is combined with a model for viscous transport. This provides exact treatment of viscous inhomogeneous effects, and enables consistent imposition of the no-slip condition in a particle framework. The method of elliptic relaxation is combined with additional boundary conditions and with the generalized Langevin model to provide an analogy for the near-wall fluctuating continuity equation. This provides adequate representation of the near-wall anisotropy of the Reynolds stresses. The model is implemented with a p.d.f./Monte Carlo simulation for the joint p.d.f. of velocity and turbulent frequency. Results are compared with DNS and experimental profiles for fully developed turbulent channel flow.