Lattice Boltzmann Method

The Boltzmann method on the network (LBM: Lattice Boltzmann Method) being a relatively recent and original numerical method which was born in the early 90s.

It initially came from the Network gas method, from the theory of cellular automata and based on the formalism of statistical physics.

It is no longer interested in macroscopic quantities (speed, pressure, density), but directly in the distribution of the different particles constituting a fluid. We then speak of mesoscopic representation. This makes it competitive with other conventional methods such as finite volumes, finite elements and finite differences.

The interest of LBM lies above all in the simplicity and locality of its algorithm, thus making its parallelization easy and efficient. Very quickly, the LBM is used for unsteady and incompressible CFD calculations.

Consequently, this method makes it possible to simulate the behavior of a fluid governed by the weakly compressible unsteady Navier-Stokes equations. Consequently, as long as the Mach number of the flow remains sufficiently low, the LBM can be used for the study of unsteady and incompressible flows.

It is important to be able to situate its performance in relation to that of the classical numerical methods used to simulate and reproduce flows with heat exchange.