Preliminary LBM study of hydrodynamic problems

The Lattice Boltzmann methods (LBM) were developed for the lattice gas automata (LGA) (see [1], [2]), more recently they have been used to study a variety of fluid dynamic problems. Differently from the classical CFD methods that solve the macroscopic variables u and ? in the Navier Stokes equations, the LBE approaches solves the kinetic equation for the particle velocity distribution function f(x, ?, t) in which ? is the particle velocity vector, x is the spatial position vector and t is the time. The macroscopic function ? and ?u are obtained from the evaluation of the hydrodynamic moments of the distribution function. This approach was first proposed by Qian et al. [3], Chen et al. [4], and dHumieres [5] and it is becoming more common because of the flexibility of the method to deal with compressible and incompressible flows and because it does not need any iterative solver for the pressure equations. More recently it has also been adapted to problems with a free surface, even though these applications are still limited. This work aims to study to application of this method to naval problems, through the analysis of classical test cases in 2D.