Projet subventionné par la Communauté Française de Belgique dans le cadre du programme d’Actions de Recherche Concertée (ARC-2002).

Direct Numerical Simulation and Large Eddy Simulation of general planar and axisymmetric turbulent flows

Simulation numérique directe et simulation des grandes échelles d’écoulements turbulents dans des géométries planes ou de révolution générales

The complete description of hydrodynamic turbulence requires the resolution of a range of scales that is known to increase very rapidly with the turbulent intensity. Direct numerical simulations (DNS) are thus restricted to moderately turbulent flows. However, the detailed characterisation of every excited mode is unnecessary to describe the large scale turbulence. This has prompted the derivation of large eddy simulations (LES). This numerical technique is based on the application of a spatial filter to the Navier-Stokes equation. The resulting equation can then be simulated using a coarser grid since the fluctuations with small characteristic scales are filtered out. However, the LES equation contains an unknown subgrid scale stress tensor that needs to be modelled. This term accounts for the effects of the unresolved small scales on the resolved scales.

The essential objective of the proposed work is to develop a parallel incompressible numerical solver for general planar and axisymmetric turbulent flows and to use it for assessing various LES methodologies. The same code will be used for performing both DNS and LES runs for the same geometries. To provide the required geometrical flexibility while exploiting the flow periodicity in the transverse direction, a discrete model combining an in-plane unstructured grid finite element representation and a Fourier spectral representation in the periodic direction is selected.

This computational platform will then be used as a workbench for the evaluation of various LES models. Classical (e.g. Smagorinsky) and advanced subgrid scale models will be implemented and tested. A particular attention will be devoted to ensemble dynamic models, which consist in evaluating the coefficients appearing in subgrid scale models dynamically using several independent realisations of the turbulent flow. Advanced artificial wall boundary conditions will also be investigated. Attention will be concentrated to the application of an artificial wall boundary condition inside the flow at some distance from the wall, using information from the core flow (inside the computational domain) and from a simple model of the unresolved wall region.

An essential feature of the proposed project is to make heavy use of parallel computing using an inexpensive distributed memory parallel machine made out of commodity hardware. Both the ensemble dynamic LES models and the solver numerical scheme are particularly suited for this purpose. This will make it possible to simulate flow problems that are out of reach of the research group present computational resources.