Simulation of two-dimensional high reynolds number wake flows with the use of filtered lagrangian navier-stokes equations

Abstract

This work presents a method for numerical simulation of viscous fluid flows based on the use of filtered Lagrangian Navier-Stokes equations. It is based on the hypothesis that the small scale motions are responsible for the homogenization of the physical properties in infinitesimal fluid parcels through a mixing process, mathematically expressed as a spatial filter, which implicitly works as an averaging operator. When the filter was applied to the Navier-Stokes equations for incompressible flows, in the Lagrangian frame of reference, the functional form of the resulting equations was preserved, and the number of unknowns remained the same as the number of available equations, therefore circumventing the need of an explicit subgrid scale model. The method was validated by performing two-dimensional simulations of high Reynolds number wake flows. It was verified that the main large scale characteristics of the flows were properly replicated.