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

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