RECENT ADVANCES IN THE THEORY OF THE LATTICE BOLTZMANN EQUATION

In the recent years, a new type of fully discrete Boltzmann equation, arising from the micro-dynamics of Lattice Gas, i.e. a special a class of cellular automata specifically designed to simulate hydrodynamical behaviour [1], has proved to perform quite competitively for the numerical simulation of a wide variety of complex hydrodynamical phenomena. This special type of Boltzmann equation, normally referred to as Lattice Boltzmann Equation (LBE), has in fact successfully been employed in the simulation of a wide span of hydrodynamical regimes, ranging from laminar flows in porous media to fully developed turbulent flows [2]. In this paper, we present some recent developments in the theory of LBE together with a quantitative discussion on the possibility to extend LBB to the domain of two-dimensional magneto-hydrodynatnics.