Lattice kinetic methods in fluid turbulence
This research area aims at a detailed investigation of some aspects of the lattice Boltzmann method (LBM), a rather new modeling approach for incompressible fluid flow problems. Classically, this field is dominated by computational fluid dynamics (CFD), that tackles the set of non linear partial differential equations known as the Navier-Stokes equations, derived by continuum mechanics considerations and based on conservation laws. LBM is another route to treat fluid problems that has emerged over the last decade. It uses microscopic models and mesoscopic kinetic equations. The basic idea of LBM consists in looking at the collective behavior of microscopic particles that collide and move. The kinetic essence of LBM brings three key characterisctics to numerical modelization: First, the convection operator is linear and resembles the particular derivative of continuum mechanics. This is favorable for parallel computing. Second, the incompressible Navier-Stokes equations are obtained in the incompressible limit of the LBM. Third, the LBM requires a minimal set of velocities in the phase space.
Whilst LB methods have already known a great success in the treatment of fluids with complicated physics, like viscoelastic fluids or two-phase flows, they have only started to establish themselves in the difficult topic of turbulence modeling. This topic addresses the problem of describing fluids at very high Reynolds numbers (high velocities, resp. low viscosities). From a computational point of view, the challenge resides in simulating a coarse grained laminar field and describing the unresolved subgrid quantities by an appropriate model. Doing so is the only way of obtaining a simulation that is feasible in terms of computation time and memory need.
One prospect of the research area is the investigation of possible frameworks for the formulation of LB turbulence theories. The work will be accompanied by a set of numerical validations, which on its turn will demand some effort in the development of specific techniques for parallel computing.
The following picture shows a 2D-cut through the vorticity field of a turbulent, homogeneous and isotropic simulation: