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:

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

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.

References

• S. Succi (2001). The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press. ISBN 978-0-19-850398-9.