Effects of incompressibility on the elimination of parasitic currents in the lattice Boltzmann equation method for binary fluids

Discretization errors in the computation of the intermolecular force in the lattice Boltzmann equation (LBE) method cause parasitic currents. A slight imbalance in the interfacial stresses due to truncation errors initiates the parasitic currents. It was shown that these currents could be eliminated to round-off if the potential form of the intermolecular force for non-ideal gases was used with compact isotropic discretization. In the present work, a formulation of the intermolecular forces for binary fluids and the role of incompressibility on parasitic currents are examined. A two-distribution function LBE method is proposed in which the incompressibility is enforced by the pressure evolution equation. As long as the intermolecular force is expressed in the potential form, the incompressible LBE method for binary fluids is able to eliminate parasitic currents.