# Bhatnagar–Gross–Krook operator

(Redirected from Bhatnagar-Gross-Krook)

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:

${\displaystyle \Omega _{i}=-\tau ^{-1}(n_{i}-n_{i}^{EQ})}$

where ${\displaystyle n_{i}^{EQ}}$ is a local equilibrium value for the population of particles in the direction of link ${\displaystyle \mathbf {e} _{i}}$ The term ${\displaystyle \tau }$ 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.[1]