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A new finite volume algorithm has been developed to solve a variety of flows by using large eddy simulation and direct numerical simulation. This finite volume algorithm was developed using a dual time stepping approach with a preconditioning technique and a new factorization implementation. The method takes the advantage of pressure-based and density-based meth­ ods. Thus, it provides an efficient way to numerically solve the Navier-Stokes equations at the low Mach numbers. The implementation of the numerical scheme was validated by obtain­ ing solutions to a number of flows including turbulent boundary layers with or without heat transfer, turbulent boundary layers subjected to free stream turbulence, and supersonic adia­ batic turbulent boundary layers. Good agreement between the present results and benchmark results in the literature was achieved. In order to generate the inflow conditions for the simulation of turbulent boundary layers, a dynamic recycling method was proposed. It is an improvement over the recycling method proposed by Lund et al., and dramatically reduces the starting-transients of the numerical sim­ ulations. In addition, a characteristic boundary condition method was suggested for the outlet boundary conditions of external wall shear flows. Such a non-reflecting boundary condition is a modification of the method introduced by Poinsot and Lele (1992). With the new numerical method and boundary condition technique it is possible to investi­ gate the statistics of turbulence with greater accuracy. Thus, the fluid physics of three different turbulent boundary layers are discussed. These are a turbulent boundary layer without heat transfer, a turbulent boundary layer on a heated wall, and an adiabatic supersonic turbulent boundary layer at Mach number 1.8. The three-dimensional two-point correlations and the one-point turbulent structure tensors of a incompressible turbulent boundary layer have been

The numerical simulation of turbulent boundary layers and film cooling