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Article | REF: BM5220 V1

Introduction to the Lattice Boltzmann Method for Fluid Mechanics

Authors: Sylvain MARTIN, Olivier BONNEFOY

Publication date: December 10, 2019

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2. Towards the Bolzmann network method (LBM)

2.1 Introduction of the linearized collision term

The Boltzmann equation describes the temporal and spatial evolution of the f function, with a highly complex collision term. However, this distribution tends towards a known equilibrium. With this in mind, it's tempting to simplify the collision term. Indeed, for a distribution close to equilibrium, it is possible to linearize the collision, i.e. to consider that the function f evolves linearly towards equilibrium:

df dt=∂f∂t+
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