Lattice Boltzmann method

The lattice Boltzmann method simulates fluid flow by evolving discrete particle-distribution functions through local collision and streaming steps on a lattice.

Lattice Boltzmann equation: A discrete kinetic equation that updates particle-distribution functions through collision and transport. It expresses the method’s evolution rule in mathematical form.
Distribution function (kinetic theory): A function describing the density of particles across position and velocity. The method discretizes this kinetic description into populations at lattice sites.
Computational fluid dynamics: The numerical study of fluid motion using computational models. The lattice Boltzmann method is an alternative formulation within this field.
Finite volume method: A numerical method that conserves quantities by balancing fluxes across cell boundaries. It solves macroscopic conservation laws directly rather than evolving particle populations.
BGK collision operator: A single-relaxation-time approximation that drives distributions toward local equilibrium. It supplies the simplest widely used collision step.
D2Q9: A two-dimensional lattice velocity set with nine discrete directions, including rest. It is a standard choice for two-dimensional simulations.
Porous medium: A material containing interconnected pores through which fluids can flow. Local lattice updates handle intricate pore geometries in flow simulations.
Finite difference method: A numerical method that approximates derivatives using values on a discrete grid. It discretizes fluid equations in a different way from lattice-based kinetic updates.
Streaming (lattice Boltzmann method): The lattice Boltzmann update that moves each population to a neighboring lattice site along its velocity direction. It is the transport half of the method’s update cycle.
D3Q19: A three-dimensional lattice velocity set with nineteen discrete directions, including rest. It is a common velocity stencil for three-dimensional flows.

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