Publication record · 18.cifr/1992.chen.lbm-navier-stokes

Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method

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Hudong Chen (Thinking Machines Corporation), Shiyi Chen (Thinking Machines Corporation), William H. Matthaeus (Bartol Research Institute)

RAI18.cifr/1992.chen.lbm-navier-stokes

Physical Review A· 1992· doi:10.1103/PhysRevA.45.R5339

A lattice-gas Boltzmann method is presented that uses a single-time relaxation (BGK) collision operator to recover the Navier-Stokes equations in the hydrodynamic limit. The approach eliminates the velocity-dependent pressure and statistical noise inherent in lattice-gas automata, and the kinematic viscosity is directly controlled by the relaxation parameter.

lattice BoltzmannNavier-StokesBGKD2Q9computational fluid dynamics

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Lattice-gas automata required exponentially complex collision tables, ensemble averaging to suppress noise, and suffered from velocity-dependent pressure. This work provides a clean, efficient alternative — the lattice Boltzmann BGK method — that reproduces Navier-Stokes without those artifacts.

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This paper shows that a BGK collision operator on a D2Q9 lattice directly recovers the incompressible Navier-Stokes equations through a Chapman-Enskog expansion, eliminating the statistical noise and non-Galilean pressure of earlier lattice-gas automata. Kinematic viscosity is analytically set by the single relaxation time tau, giving clean control over Reynolds number.

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