LBM Theory

LBM (LATTICE BOLTZMANN METHODS)

LBM is a numerical approach for analyzing fluid flow using particle distribution functions. These distribution functions represent the density distribution of particles in the physical space, each of which have a specific velocity and density. These distribution functions are used to calculate the macroscopic flow properties such as fluid density, velocity, and temperature. LBM numerically solves the Boltzmann transport equation to simulate the time-evolution of the particle distributions within the computational domain and is fundamentally different from the traditional finite volume method (FVM) which solves the Navier-Stokes equations. Because the LBM discretizes the computational domain with a Cartesian lattice, it requires a much simpler preprocessing step than traditional CFD methods do and can be easily applied to simulate flows with complex geometries. Furthermore, because it is a mesoscopic approach, it can be more easily applied to microscopic flows which traditional CFD tools have difficulty simulating.

Historically, the LBM originates from the lattice gas automata (LGA). In addition to its vastly simple preprocessing, the local nature of computations makes the LBM applicable for hugely parallelized computational architectures. This computational efficiency is a competitive advantage of the LBM compared to traditional CFD methods and has garnered much interest of the research community. LBM research has been very active during the last couple decades, and this research activity has enabled the LBM to overcome its traditional weak compressibility limit to be able to analyze compressible flows, and supersonic flows. Furthermore, LBM continues to expand its applicability with applications to heat transfer, multiphase flows, acoustics, aeroacoustics, as well as fluid-structure interactions via coupling with DEM and FEM solvers.