Lattice Boltzmann Method
June 2024
The lattice Boltzmann method (LBM) is a computational fluid dynamics (CFD) method for simulating macroscopic fluid flows. The cool thing about the LBM is that the method actually solves the microscopic evolution of particle speed distributions at each point in space, and the macroscopic fluid behaviour emerges from this.
In fact, it can even be shown mathematically that the macroscopic behaviour is described by none-other than the Navier-Stokes (NS) equations given the microscopic behaviour described by the Boltzmann equation . On the one hand this is perhaps not too surprising; ultimately fluids are composed of molecules, or atoms, with trajectories evolving according to Newtonian mechanics. So if we successfully summarize their behaviour in a course-grained fashion we should expect the NS equations to emerge. On the other hand, I remember being blown away the first time that I learned you could prove that the macroscopic behaviour is governed by the NS equations.
Fluid flow is a fantastic example of how macroscopic behaviour can emerge from microscopic interactions.
In the following articles I will introduce the Boltzmann equation, how to discretize & simulate it, and show some simulation results.