Stability Analysis of Inter-Molecular Interaction Schemes in Multi-Phase Lattice Boltzmann Method

In this paper, we present a comparative analysis of popular intermolecular forcing schemes in which their differences and similarities are identified. The results indicate that the stability of each scheme depends on three factors, density ratio, relaxation time, and reduced temperature, and it is independent of the physics of the problem. In any scheme except for Kupershtokh’s scheme (scheme 3-b) for t/Dt ³ 1.5 the gas density (lower density) would get larger than the critical density and the density field will diverge or get to a non-physical value. Then by fixing the relaxation time and implementing different reduced temperatures when T/T-c ³ 0.9 implementing C-S EOS for all schemes except for the one introduced by He et al. (scheme 2-d) gas density (lower density) would get larger than the critical density and again the density field will diverge or get to a non-physical value. Variation of the physical conditions of the problem and moving the droplet from the center of the field and placing it next to the wall, wouldn’t cause significant variation in the equilibrium density field, and this difference in equilibrium density is negligible. However, this may affect the dependence of Kupershtokh’s scheme on relaxation time. Furthermore, the effect of forcing schemes on the contact angle between the wall and the bubble has been investigated. Results of schemes 1-a and 2-d are somehow identical and the difference between contact angle computed with these schemes and ones computed by schemes 3-a and 3-b is around 21 percent.