Bhatnagar-Gross-Krook
Encyclopedia
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:
where
is a local equilibrium value for the population of particles in the direction of link 
The term 
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.
Boltzmann equation
The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...
and in the Lattice Boltzmann method
Lattice Boltzmann methods
Lattice Boltzmann methods is a class of computational fluid dynamics methods for fluid simulation. Instead of solving the Navier–Stokes equations, the discrete Boltzmann equation is solved to simulate the flow of a Newtonian fluid with collision models such as Bhatnagar-Gross-Krook...
, a Computational fluid dynamics
Computational fluid dynamics
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...
technique. It is given by the following formula:
where
is a local equilibrium value for the population of particles in the direction of link The term is a relaxation time, and related to the viscosity.The operator is named after Prabhu L. Bhatnagar
Prabhu Lal Bhatnagar
Prabhu Lal Bhatnagar , commonly addressed as P. L. Bhatnagar, was an Indian mathematician known for his contribution to the Bhatnagar-Gross-Krook collision model used in Lattice Boltzmann methods .-Early years:...
, Eugene P. Gross, and Max Krook
Max Krook
Max Krook was an American mathematician and astrophysicst.He is remembered for his contribution to the Bhatnagar-Gross-Krook model.-Selected works:...
, the three scientists who introduced it in a paper in Physical Review
Physical Review
Physical Review is an American scientific journal founded in 1893 by Edward Nichols. It publishes original research and scientific and literature reviews on all aspects of physics. It is published by the American Physical Society. The journal is in its third series, and is split in several...
in 1954.