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 methods. Thus, it provides an efficient way to numerically solve the Navier-Stokes equations at the low Mach numbers. Meanwhile, to generate the inflow conditions for the simulation of turbulent boundary layers, a dynamic recycling method was proposed. In addition, a characteristic boundary condition method was suggested for the outlet boundary conditions of external wall shear flows. The implementation of the methods was validated by obtaining 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 adiabatic turbulent boundary layers. Good agreement between the present results and benchmark results in the literature was achieved. With the new numerical method and boundary condition technique it is possible to investigate 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 incompressible turbulent boundary layer study focused on the two-point correlation and the anisotropy. The compressible turbulent boundary layers study, that is, the low Mach number turbulent boundary layer with strong heat transfer and the supersonic turbulent boundary layer, is concerned with the strong Reynolds analogy, Van Driest transformation, and the applicability of Morkovin's hypothesis. Large eddy simulation is applied to an example discrete hole film cooling configuration. The computational domain included the coolant supply tube as well as the main mixing region. A tube L/D of 8 and an injection angle of 35 degrees was employed for two different simulations: one was with a blowing ratio of 0.5, and the other was with a blowing ratio of 0.362.