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"Available energy is the main object at stake in the struggle for existence and the evolution of the world."
Ludwig Eduard Boltzmann (1844 - 1906) “Father” of Statistical Mechanics
The Boltzmann Lattice Boltzmann Method (LBM) is a relatively new and original numerical method that was developed in the early 1990s. It is no longer interested in macroscopic quantities (speed, pressure, density), but directly in the distribution of the different particles constituting a fluid. This is called mesoscopic representation. This makes it competitive with other conventional methods such as finished volumes, finite elements and finite differences. It is originally derived from the gas on grid method, from the theory of cellular automata and based on the formalism of statistical physics.
The interest of LBM lies above all in the simplicity and locality of its algorithm, making its parallelization easy and efficient. Very soon, the LBM is used for unsteady and incompressible CFD calculations.
Therefore, this method allows to simulate the behavior of a fluid governed by the low compressible unsteady Navier-Stokes equations. Therefore, as long as the Mach number of the flow remains low enough, LBM can be used for the study of unsteady and incompressible flows. It is important to be able to situate its performances in relation to those of the conventional numerical methods used to simulate and reproduce flows with heat exchange.
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