Direct numerical simulation of incompressible turbulent flows

The paper discusses recent achievements of direct numerical simulation (DNS) of incompressible flows. The various spatial discretization techniques which can be used in the case of simple or complex geometry are referred to, along with suitable time advancement schemes. The advantage of using a staggered variable arrangement and efficient Poisson solvers is stressed before initial and boundary conditions for inflow, entrainment and outflow boundaries are discussed. Comments on the spatial resolution required for DNS and on the use of zonal embedded grids to reduce the computational effort complete the part on numerical aspects. A few examples are then given where DNS serves to study the physics of turbulent flows. The first is fully developed flow through solid and permeable pipes. Wall permeability turns out to be a means to model wall roughness. Striking changes in the turbulence structure are observed near rough walls. The second example deals with flow separation in sudden expansions of solid and permeable pipes. It is found that the free shear layer surrounding the re-circulation zone experiences a markedly different downstream development if the incoming flow is confined by rough walls. The reattachment length is reduced. At the same time the amplification rates of the maximum values of the Reynolds stress components in the mixing layer are lower than those in the solid wall configuration. The results underline the importance of the wall blocking effect. The third example concerns fully developed flow through curved and coiled pipes. Strong secondary flow generates complex mean flow fields and six nonzero Reynolds stress components contributing to the production of turbulent kinetic energy. This renders the flow unpredictable by two-equation models and thus a challenge to turbulence modellers.