Lehmer matrix: Difference between revisions

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The '''Bhatnagar–Gross–Krook operator''' (abbreviated '''BGK operator''') term refers to a collision [[operator (mathematics)|operator]] used in the [[Boltzmann Equation]] and in the [[Lattice Boltzmann methods|Lattice Boltzmann method]], a [[Computational fluid dynamics]] technique. It is given by the following formula:
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:<math>\Omega_i=-\tau^{-1}(n_i-n_i^{EQ})</math>
 
where <math>n_i^{EQ}</math>  is a local equilibrium value for the population of particles in the direction of link <math>\mathbf{e}_i</math> The term <math>\tau</math> is a relaxation time, and related to the viscosity.
 
The operator is named after [[Prabhu Lal Bhatnagar|Prabhu L. Bhatnagar]], [[Eugene P. Gross]], and [[Max Krook]], the three scientists who introduced it in a paper in [[Physical Review]] in 1954.<ref>
{{cite journal
|author=P.L. Bhatnagar, E.P. Gross, M. Krook
|year=1954
|title=A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
|journal=[[Physical Review]]
|volume=94 |pages=511–525
|doi=10.1103/PhysRev.94.511
|bibcode=1954PhRv...94..511B
|issue=3
}}</ref>
 
==References==
{{reflist}}
*{{cite book
|author=S. Succi
|year=2001
|title=The Lattice Boltzmann Equation for Fluid Dynamics and Beyond
|publisher=[[Oxford University Press]]
|isbn=978-0-19-850398-9
}}
 
{{DEFAULTSORT:Bhatnagar-Gross-Krook operator}}
[[Category:Statistical mechanics]]
[[Category:Computational fluid dynamics]]
 
 
{{fluiddynamics-stub}}

Latest revision as of 15:19, 11 March 2014

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