Bhatnagar-Gross-Krook

The Bhatnagar-Gross-Krook (abbreviated BGK) 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:

:$Omega\_i=-\; au^\{-1\}(n\_i-n\_i^\{EQ\})$

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

The operator is named after Prabhu Lal Bhatnagar, E. P. Gross, and Max Krook, the three scientists who introduced it in a paper in Physical Review in 1954. [P. L. Bhatnagar, E. P. Gross, and M. Krook, "A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems", "Phys. Rev." 94, 511-525 (1954).]

References

Sauro Succi, "The Lattice Boltzmann Equation for Fluid Dynamics and Beyond", Oxford University Press, 2001