ANALYSIS OF THE LATTICE BOLTZMANN TREATMENT OF HYDRODYNAMICS

It is shown that the lattice-Boltzmann model can be made to obey the three-dimensional thermal Navier-Stokes equations by fixing 26 moments of the equilibrium distribution function. This can be achieved on a cubic lattice with particle velocities connecting each lattice site to its first, second and third nearest neighbors; however, this minimal model is not linearly stable in the limit of low transport coefficients. Additional particle velocities must be selected to achieve linear stability.