Wall-boundary conditions in probability density function methods and application to a turbulent channel flow

An application of a probability density function (PDF), or Lagrangian stochastic, approach to the case of high-Reynolds number wall-bounded turbulent flows is presented. The model simulates the instantaneous velocity and dissipation rate attached to a large number of particles and the wall-boundary conditions are formulated directly in terms of the particle properties. The present conditions aim at reproducing statistical results of the logarithmic region and are therefore in the spirit of wall functions. A new derivation of these boundary conditions and a discussion of the resulting behavior for different mean variables, such as the Reynolds stress components, is proposed. Thus, the present paper complements the work of Dreeben and Pope [Phys. Fluids 9, 2692 (1997)] who proposed similar wall-boundary particle conditions. Numerical implementation of these conditions in a standalone two-dimensional PDF code and a pressure-correction algorithm are detailed. Moments up to the fourth order are presented for a high-Reynolds number channel flow and are analyzed. This case helps to clarify how the method works in practice, to validate the boundary conditions and to assess the model and the code performance.