BhatnagarGrossKrook
The Bhatnagar–Gross–Krook (BGK) model is a simplified collision operator used in the kinetic theory of gases. Introduced in 1954 by Bhatnagar, Gross and Krook, it replaces the Boltzmann collision integral with a single relaxation term that drives the one-particle distribution function toward local equilibrium on a characteristic time scale. The model is widely used as a tractable alternative to the full Boltzmann equation and as a foundational component in lattice Boltzmann methods.
In mathematical form, the BGK model modifies the Boltzmann equation to
df/dt + v · ∇_x f = (f_eq − f)/τ,
where f = f(x, v, t) is the distribution function in phase space, f_eq is the local Maxwellian
The BGK model is valued for its simplicity and computational efficiency, and it forms the basis for
See also Boltzmann equation, lattice Boltzmann method, H-theorem.