7 - Introduction to Direct Numerical Simulation
Published online by Cambridge University Press: 06 July 2010
Summary
Abstract
Direct numerical simulation (DNS) of the three-dimensional Navier–Stokes equations provides data to study turbulence, including quantities that cannot be accurately measured experimentally. With the advent of massively parallel computing the range of flows that can be treated by DNS is increasing. This chapter reviews the development of DNS methods and the fundamental limitation on simulation Reynolds number which arises from the basic nature of turbulence. Particular attention is then given to methods of validation of simulations to attain sufficient confidence in the data for application to the turbulence closure problem. Different uses for the data are outlined using examples taken from simulations of channel and wake flows.
Introduction
Direct solution of the Navier–Stokes equations has been made possible by the development of fast digital computers, with the first simulations of isotropic turbulence appearing in the 1970s. Since that time there have been notable advances in algorithms relating to spectral methods and high-order finite difference schemes. However, for the most part simulations of more complicated flows have depended for their feasibility on further developments in computer hardware. An illustration of the recent rate of increase in computer performance is given by Figure 1, which shows data from the Top500 supercomputer list (http://www.netlib.org/benchmark/top500.html). On this graph we show the maximum achieved performance for the ‘linpack’ benchmark (Rmax) of the computers rated number 1 and number 500, together with an average over the top 500 supercomputer sites from the June census each year. The slope of the curve for the average machine shows performance increasing as exp(0.58t) where t is the time in years. This corresponds to roughly an order of magnitude increase every four years, or a doubling every 1.2 years. One needs to interpret some aspects of the curves with care. The peak performance for the linpack benchmark is not very closely approached with fluid mechanics codes, and how close one can get depends on the manufacturer (and particularly upon how much they have optimised the machine for this particular benchmark). The recent rate of performance improvement may also be atypical because of the recent move to massively parallel processing (MPP). Whether a code can effectively use the enhanced capacity depends on the application. However, even taking these issues into account it is clear that there is an ongoing exponential growth in computing capacity which shows no signs of slowing down in the near future. In particular the Accelerated Strategic Computing Initiative (ASCI) project in the USA is driving the performance of the largest computers further forward.
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- Closure Strategies for Turbulent and Transitional Flows , pp. 248 - 266Publisher: Cambridge University PressPrint publication year: 2002
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