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

T. Lafarge (1) , Pierre Boivin (2) , N. Odier (1) , B. Cuenot (1)

1 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
2 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres

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 p=f(ρ,ϕ), 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.

Domaines: Mécanique des fluides [physics.class-ph]

T. Lafarge, Pierre Boivin, N. Odier, B. Cuenot. Improved color-gradient method for lattice Boltzmann modeling of two-phase flows. Physics of Fluids, 2021, 33 (8), pp.082110. ⟨10.1063/5.0061638⟩. ⟨hal-03324224⟩