An incompressible separated transitional boundary-layer flow on a flat 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 finite difference formulae are used in the periodic direction. The entire transition process has been elucidated and vortical structures have been identified at different stages during the transition process. Efficient numerical methods for the large-eddy simulation (LES) of turbulent flows in complex geometry are developed. The methods used are described in detail: body-fitted co-ordinates with the contravariant velocity components of the general NavierStokes 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 flows is due to the solution of a Poisson equation for pressure. This is especially true for flows in complex geometry. Fourier techniques can be employed to speed up the pressure solution significantly for a flow which is periodic in one dimension. With simple conditions fulfilled, it is possible to Fourier transform a discrete elliptic equation such as the Poisson equation for the pressure field, decomposing the problem into a set of two-dimensional problems of similar type (Poisson-like). Even when a complex geometry and body-fitted curvilinear co-ordinates are used in the other two dimensions, as in the present case, the resulting Fourier-transformed 2D problems are much more efficiently solved than the 3D problem by iterative mean
