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 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.
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⟩
Journal: Physics of Fluids
Date de publication: 01-01-2021