On the lattice Boltzmann method for multiphase flows with large density ratios

An analysis of the lattice Boltzmann (LB) method for multiphase flows with large density ratios is presented. It is shown that for incompressible, multiphase LB methods, the divergence-free condition is not satisfied within the formal accuracy of the LB method, when the density ratio between the two phases is large enough. The discrete differentiation-by-parts rule is responsible for this error. A new multiphase LB method to resolve this issue is proposed.