Background

The foundations of DNS were laid at the National Center for Atmospheric Research in 1972 by Orszag & Patterson [12], who used spectral methods to perform a 32³ computation of isotropic turbulence at a Reynolds number of 35 (based on Taylor microscale). The next major step was taken by Rogallo [15] in 1981, who combined a transformation of the governing equations with an extension of the Orszag-Patterson algorithm to compute homogeneous turbulence subjected to mean strain. The results were compared to theory and experimental data and used to evaluate several turbulence models which set the standard for DNS of homogeneous turbulence. The earliest computed flows were inhomogeneous in only one direction. The computing resources in the late 1970's did not allow DNS of wall-bounded turbulence; however, coarse-grid computations of free-shear layers could be performed. It was not until 1987 that the DNS of the plane channel flow was performed [6]. The next major step was taken by Spalart [16], who developed an ingenious method to compute the turbulent flat-plate boundary layer under zero and favorable pressure gradients. Computing flows that are inhomogeneous in the streamwise direction required that the turbulence be specified at the inflow plane. A recent advance has been the development of methods to specify this inflow turbulence, as a result of which reasonably complex flows, e.g. the flow over a backstep (Le & Moin [7] in 1994), and flat plate boundary layer separation (Na & Moin [11] in 1996) have been computed.

In contrast to its incompressible counterpart, DNS of compressible turbulent flow has been fairly recent. The DNS of homogeneous compressible turbulence was initiated in 1981 by Feiereisen et al. [3], but a serious study of compressible homogeneous turbulence (isotropic and sheared) was undertaken only a decade later. Wall-bounded flows such as the compressible channel and turbulent boundary layer have only recently been attempted. Recently, DNS has also examined high-speed turbulent mixing layers and the interaction of shock waves with turbulence. An exciting new development has been the field of computational aeroacoustics, where both the fluid motion and the sound it radiates are directly computed using DNS.

In tracing the evolution of DNS over the past decade, it is observed that the complexity of the computed flows has noticeably increased, but that their Reynolds number is still low. Another development has been the increased investigation of turbulence physics by computing idealized flows that cannot easily be produced in the laboratory. As the geometry of the flows has evolved, so have the numerical methods. These changes have been accompanied by a significant improvement in computer hardware. Currently available parallel machines like the 64 processor SP-2 are about 100 times faster than the 64 processor ILLIAC-IV used in the early 1980s.