Lattice BGK Models for Navier-Stokes Equation

TLDR

The authors propose lattice BGK models as an efficient alternative to lattice gases and the lattice Boltzmann equation for simulating fluid dynamics. The scheme derives the Navier–Stokes equations from a kinetic BGK equation using a chosen equilibrium distribution and a relaxation parameter that controls stability. The model is noise‑free, Galilean invariant, has velocity‑independent pressure, and simulations confirm the correct speed of sound and shear viscosity.

Abstract

We propose the lattice BGK models, as an alternative to lattice gases or the lattice Boltzmann equation, to obtain an efficient numerical scheme for the simulation of fluid dynamics. With a properly chosen equilibrium distribution, the Navier-Stokes equation is obtained from the kinetic BGK equation at the second-order of approximation. Compared to lattice gases, the present model is noise-free, has Galileian invariance and a velocity-independent pressure. It involves a relaxation parameter that influences the stability of the new scheme. Numerical simulations are shown to confirm the speed of sound and the shear viscosity.