Optimal Unstructured Meshing for Large Eddy Simulations

An attempt is made to provide a criterion for optimal unstructured meshing for LES from the knowledge of different turbulence lengthscales. In particular, the performance of a grid based on the Taylor microscales for turbulent channel flow, is investigated, with the final view of facilitating an a priori determination of the mesh resolution required for LES. The grid dictated by the Taylor microscales is more cubical in the centre of the domain than the typical empirical LES grids. Furthermore, it is as fine in the spanwise direction as it is in the wall normal direction. Empirical LES grids, currently widely used, have a very fine (approximately four times finer) wall normal resolution and a coarse (about twice as course) streamwise resolution as compared to a grid based on the Taylor microscales. A remarkable feature is that the mean velocity and streamwise component of fluctuating velocity (classically over-predicted in coarse grid LES) and the wall normal fluctuating velocity are well reproduced on the new grid. The attempt of building an unstructured LES grid based on the Taylor microscale has been found very successful. However, as the Reynolds number is increased this sort of requirement might be excessive and eventualy a criterion such as one tenth of the integral lengthscale could be sufficient.