Analysis of force treatment in lattice Boltzmann equation method

Abstract In lattice Boltzmann equation (LBE), density distribution function is apparently relaxed to a given state f i ( gs ) ( ρ , u ∗ ) with an external/internal force, here ρ is fluid density and velocity u ∗ can be different with physical velocity u . In the literature, it was shown that f i ( 0 ) should be f i ( gs ) ( ρ , u ∗ ) , however, present work shows that f i ( 0 ) is f i ( eq ) ( ρ , u ) with different force scheme in single relaxation time LBE. The corresponding error terms are analyzed at Navier–Stokes level, and numerical results confirm our theoretical analysis.