Description of a 3D vortical flow by a Lattice Boltzmann Method

The Lattice Boltzmann Method (LBM) has been introduced about 20 years ago (see [1] and [2]), but only the recent development of a multiple-relaxation-time (MRT) collision model [3] has allowed its application to a wide range of Reynolds numbers. The comparison of its results with those obtained with a DNS incompressible-flow spectral element solver has also shown that it can correctly capture the details of the fluid turbulence [4], preserving its basic features of simplicity, flexibility and intrinsic parallelism. For these last features and for its enhanced suitability to deal with viscous flows, the LBM starts to be appealing to deal with high vorticity generated in water and its interaction with the both the solid and deformable boundaries as the air-water interface. For moving vehicles, e.g. submarines and airplanes, vorticity generation and its interaction with the downstream body part can cause boundary layer separation and transition to turbulence with a dramatic effect on the unsteady forces [5]. Here, we present the application of the MRT Lattice Boltzman model to a variety of fluid-body interaction dealing with vorticity generation and dissipation. The vorticity is either generated in 2D or 3D lid driven cavity. The computed flow features are widely compared with data available in literature. In particular, the velocity, vorticity and pressure evolution are analyzed versus the same quantities obtained with Navier-Stokes solutions or in the experiments. The results show convergence and accuracy of the LBM solver. Finally, the 3D problem of a vortex ring impacting on a flat wall is analyzed. The effects of the interaction with the solid boundary are highlighted: dissipation at low Reynolds (Re) numbers, instabilities at high Re.