Self-conditioned fields for large-eddy simulations of turbulent flows

摘要

An alternative foundation is developed for the large-eddy simulation (LES) of turbulent flows. It is based on self-conditioned fields, for example, the mean velocity field conditional on a discrete representation of the filtered velocity field. It is shown that the self-conditioned velocity field minimizes the residual kinetic energy, and that, with the ideal model, the method yields the correct one-time behaviour as determined by the Navier-Stokes equations. The approach is extended to the self-conditioned probability density function (PDF) of compositions. Compared to LES formulations based on the filtered velocity and the filtered density function, the self-conditioned field approach has several advantages: for laminar flow, and in the direct-numerical-simulation limit, the residual fluctuations are zero or exponentially small; full account is taken of the probability distribution of turbulent fields; there are no commutation issues; and there are no issues with filtering at walls, where the self-conditioned velocity is zero. The exact evolution equations for the self-conditioned velocity and composition PDF are derived. Basic models are presented, and the development of improved models is discussed.