Bhatnagar–Gross–Krook operator

Not to be confused with Bernstein–Greene–Kruskal in plasma physics, also abbreviated as BGK.

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]

References

1. 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 978-0-19-850398-9.