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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 formula

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

where ${\displaystyle n_{i}^{\text{eq}}}$ 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 an article in Physical Review in 1954.

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.

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