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 fi(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 fi(0) should be fi(gs)(ρ,u∗), however, present work shows that fi(0) is fi(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.