Bhatnagar–Gross–Krook operator

The Bhatnagar–Gross–Krook operator (abbreviated BGK operator) term refers to a collision operator used in the Boltzmann Equation and in the Lattice Boltzmann method, a Computational fluid dynamics technique. It is given by the following formula:

$\Omega_i=-\tau^{-1}(n_i-n_i^{EQ})$

where $n_i^{EQ}$ is a local equilibrium value for the population of particles in the direction of link $\mathbf{e}_i$ The term $\tau$ is a relaxation time, and related to the viscosity.

The operator is named after Prabhu L. Bhatnagar, Eugene P. Gross, and Max Krook, the three scientists who introduced it in a paper in Physical Review in 1954.