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.^[1]

References

^ P.L. Bhatnagar, E.P. Gross, M. Krook (1954). "A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems". Physical Review 94 (3): 511–525. Bibcode 1954PhRv...94..511B. doi:10.1103/PhysRev.94.511.

S. Succi (2001). The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press. ISBN 9780198503989.