PDF modeling of near-wall turbulent flows: A New model, Weak second-order scheme and a numerical study in a Hybrid configuration

Abstract: In this work, we discuss some points relevant for stochastic modelling of one- and two-phase turbulent flows. In the framework of stochastic modelling, also referred to PDF approach, we propose a new Langevin model including all viscosity effects and thus that is consistent with viscous Navier-Stokes equations. In the second part of the work, we show how to develop a second-order unconditionally stable numerical scheme for the stochastic equations proposed. Accuracy and consistency of the numerical scheme is demonstrated analytically. In the last part of the work, we study the fluid flow in a channel flow with the proposed viscous method. A peculiar approach is chosen: the flow is solved with a Eulerian method and after with the Lagrangian model proposed which uses some of the Eulerian quantities. In this way attention is devoted to the issue of consistency in hybrid Eulerian/Lagrangian methods. It is shown that the coupling is important indeed and that to couple the Lagrangian model to an Eulerian one which is not consistent with the same turbulence physics leads to large errors. This part of the work complements a recent article [Chibbaro and Minier International Journal of Multiphase flows submitted (arXiv:0912.2045)]