Improved color-gradient method for lattice Boltzmann modeling of two-phase flows

Abstract

This article presents a revised formulation of the color gradient method to model immiscible two-phase flows in the lattice Boltzmann framework. Thanks to this formulation, the color-gradient method is generalized to an arbitrary Equation of State under the form relieving the nonphysical limitation between density and sound speed ratios present in the original formulation. A fourth-order operator for the equilibrium function is introduced, and its formulation is justified through the calculation of the 3rd order equivalent equation of this numerical scheme. A mathematical development demonstrating how the recoloration phase allows us to solve a conservative Allen-Cahn equation is also proposed. Finally, a novel temporal correction is proposed, improving the numerical stability of the method at high density ratio. Validation tests up to density ratios of 1000 are presented.