Direct Numerical Simulation Of Turbulent Flows

The numerical simulation of turbulent flows has a short history. About 45 years ago von Neumann (1949) and Emmons (1949) proposed an attack on the turbulence problem by numerical simulation. But one could point to a beginning 20 years later when Deardorff (1970) reported on a large-eddy simulation of turbulent channel flow on a 24x20x14 mesh and a direct simulation of homogeneous, isotropic turbulence was accomplished on a 323 mesh by Orszag and Patterson (1972). Perhaps the arrival of the CDC 6600 triggered these initial efforts. Since that time, a number of developments have occurred along several fronts. Of course, faster computers with more memory continue to become available and now, in 1994, 2563 simulations of homogeneous turbulence are relatively common with occasional 5123 simulations being achieved on parallel supercomputers (Chen et al., 1993) (Jimenez et al., 1993). In addition, new algorithms have been developed which extend or improve capabilities in turbulence simulation. For example, spectral methods for the simulation of arbitrary homogeneous flows and the efficient simulation of wall-bounded flows have been available for some time for incompressible flows and have recently been extended to compressible flows. In addition fast, viscous vortex methods and spectral element methods are now becoming available, suitable for incompressible flow with complex geometries. As a result of all these developments, the number of turbulence simulations has been increasing rapidly in the past few years and will continue to do so. While limitations exist (Reynolds, 1990; Hussaini et al., 1990), the potential of the method will lead to the simulation of a wide variety of turbulent flows. In this chapter, we present examples of these new developments and discuss prospects for future developments.