This award is to develop a better understanding of transitional turbulent flows and turbulent flows in complex geometries with heat transfer by employing direct and large eddy numerical simulations. Turbulence is one of the important unresolved problems in engineering and science. Despite the fact that there is an urgent need for better methods to predict the thermal features of turbulent flow in complex engineering systems, no workable general theory is currently available. The objectives of this proposed work are to: 1) improve subgrid-scale and numerical modeling for flows in complex geometries; 2) expand the capabilities of large eddy simulation technology to supply new information for higher Reynolds number flows. The simulations will be based on a preconditioned finite volume discretization to solve the compressible Navier-Stokes equations. This approach is novel in its use of low Mach number preconditioning applied to fully incompressible flows. The research will focus on studying by-pass and separation bubble transition and film cooling in turbines.