A primer on direct numerical simulation of turbulence - methods, procedures and guidelines

Abstract

Direct Numerical Simulation (DNS) is the branch of CFD devoted to high-fidelity solution of
turbulent flows. DNS differs from conventional CFD in that the turbulence is explicitly resolved,
rather than modelled by a Reynolds-averaged Navier-Stokes (RANS) closure. It differs from
large-eddy simulation (LES) in that all scales, including the very smallest ones, are captured,
removing the need for a subgrid-scale model. DNS can thus be viewed as a numerical
experiment producing a series of non-empirical solutions, from first principles, for a virtual
turbulent flow (see Figure 1). Its great strength is the ability to provide complete knowledge,
unaffected by approximations, at all points within the flow, at all times within the simulation
period. DNS is therefore ideal for addressing basic research questions regarding turbulence
physics and modelling. This ability, however, comes at a high price, which prevents DNS from
being used as a general-purpose design tool.
The defining characteristics of DNS stem from the distinctive characteristics of turbulence.
Because turbulence is inherently unsteady and three-dimensional, DNS requires timedependent
calculations within a three-dimensional domain.? These two features are shared
with LES (and therefore LES/RANS hybrid strategies such as detached eddy simulation
(DES)). The unique feature of DNS is associated with the manner in which turbulence is
affected by viscosity. This is responsible for the two chief drawbacks of DNS – its extreme
computational cost, and severe limitation on the maximum Reynolds number that can be
considered.

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ORCID for Richard D. Sandberg: orcid.org/0000-0001-5199-3944

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