On the Control of the Mass Errors in Finite Volume-Based Approximate Projection Methods for Large Eddy Simulations

Filtering in Large Eddy Simulation (LES) is often only a formalism since practically discretization of both the domain and operators is used as implicit grid-filtering to the variables. In the present study, the LES equations are written in the integral form around a Finite Volume (FV) Ώ rather than in the differential form as is more usual in Finite Differences (FD) and Spectral Methods (SM). Grid-filtering is therefore associated to the use of an explicit local volume average, by the way of surface flux integrals, and specific LES equations are here described. Moreover, since the filtered pressure characterizes itself only as a Lagrange multiplier used to satisfy the continuity constraint, projection methods are used for obtaining a divergence-free velocity. The choice of the non-staggered collocation is often preferable since is easily extendable on general geometries. However, the price to be paid in the so-called Approximate Projection Methods, is that the discrete continuity equation is satisfied only up to the magnitude of the local truncation error. Thus, the effects of such source errors are analyzed in FD and FV-based LES of turbulent channel flow. It will be shown that the FV formulation is much more efficient than FD in controlling the errors.