Physics:Bhatnagar–Gross–Krook operator

Short description: Collision operator used in a computational fluid dynamics technique

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:

[math]\displaystyle{ \Omega_i=-\tau^{-1}(n_i-n_i^{EQ}) }[/math]

where [math]\displaystyle{ n_i^{EQ} }[/math] is a local equilibrium value for the population of particles in the direction of link [math]\displaystyle{ \mathbf{e}_i }[/math] The term [math]\displaystyle{ \tau }[/math] 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.