Direct numerical and large-eddy simulation of complex turbulent flows

A notable trend in the direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent flows over the past two decades has been their application to multiphysics flows and highly complex geometries. This article discusses key aspects of this development for incompressible flows from the author’s perspective. Numerical errors are discussed in terms of their impact on the multiple scales of motion. A dynamic theory to predict the impact of numerical error on solutions to the LES equations is discussed, compared to actual LES, and used to comment on the various sources of numerical error. Numerical methods that are well-suited for RANS are not directly applicable to LES. An unstructured-grid numerical algorithm to perform DNS and LES in both canonical and complex engineering geometries is discussed. Key features of an unstructured overset method capable of performing DNS and LES of the flow over a large number of moving bodies in turbulent flow are presented. Flows that were considered complex in past years are now canonical; two illustrative examples are presented. The analysis of ‘big data’ is considered from a couple of perspectives: numerical issues such as finite precision error and scalability, and the ability to obtain quantitative answers to fundamental questions that would have been inconceivable a couple of decades ago. The synergy between DNS and experiments is discussed using an illustrative example. The article concludes with the author’s outlook for the field’s development.