Large-eddy simulation of separated leading-edge flow in general co-ordinates

An incompressible separated transitional boundary-layer ow on a at plate with a semi-circular leading edge has been simulated and a very good agreement with the experimental data has been obtained, demonstrating how this technique may be applied even when nite di erence formulae are used in the periodic direction. The entire transition process has been elucidated and vortical structures have been identi ed at di erent stages during the transition process. E cient numerical methods for the large-eddy simulation (LES) of turbulent ows in complex geometry are developed. The methods used are described in detail: body- tted co-ordinates with the contravariant velocity components of the general Navier{Stokes equations discretized on a staggered mesh with a dynamic subgrid-scale model in general co-ordinates. The main source of computational expense in simulations for incompressible ows is due to the solution of a Poisson equation for pressure. This is especially true for ows in complex geometry. Fourier techniques can be employed to speed up the pressure solution signi cantly for a ow which is periodic in one dimension. With simple conditions ful lled, it is possible to Fourier transform a discrete elliptic equation such as the Poisson equation for the pressure eld, decomposing the problem into a set of two-dimensional problems of similar type (Poisson-like). Even when a complex geometry and body- tted curvilinear co-ordinates are used in the other two dimensions, as in the present case, the resulting Fourier-transformed 2D problems are much more e ciently solved than the 3D problem by iterative means.