Nodes, Modes and Flow Codes

Understanding turbulent flows is a "grand challenge" comparable to other prominent scientific problems such as the large-scale structure of the universe and the nature of subatomic particles. In contrast to many of the other grand challenges, progress on the basic theory of turbulence translates nearly immediately into a wide range of engineering applications and technological advances that affect many aspects of everyday life. Numerical prediction of fluid flows is at the heart of understanding and modeling turbulence. However, such computational fluid dynamics simulations challenge the capabilities of both algorithms and the fastest available supercomputers. In 1970 Howard Emmons reviewed the possibilities for numerical modeling of fluid dynamics and concluded: "The problem of turbulent flows is still the big holdout. This straightforward calculation of turbulent flows—necessarily three-dimensional and nonsteady— requires a number of numerical operations too great for the foreseeable future." However, within a year of the publication of his article, the field of direct numerical simulation (DNS) of turbulence was initiated with the achievement of accurate simulations of wind-tunnel flows at moderate Reynolds numbers. (The Reynolds number, a dimensionless measure of the degree of nonlinearity of a flow, is defined as R = vrmsL/v, where vrms is the rms velocity, v is the kinematic viscosity of the fluid, and L is a typical length scale at which the energy maintaining the flow is input. At sufficiently high Reynolds numbers, flows become turbulent.) In the last 20 years, the field of turbulence simulation has developed in two directions. First, turbulence simulations are now regularly performed in simple geometries, and extensive databases of flow fields have been constructed for the analysis of turbulent and even laminar-turbulent transitional interactions. Second, simulations of turbulent flows in prototype complex geometries are now emerging. (See figure 1 and the cover of this issue.)