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 nonphy...

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Bibliographic Details
Published in:Physics of fluids (1994) 2021-08, Vol.33 (8), p.82110
Main Authors: Lafarge, T., Boivin, P., Odier, N., Cuenot, B.
Format: Article
Language:English
Subjects:
Color
Density ratio
Engineering Sciences
Equations of state
Fluid dynamics
Fluids mechanics
Mathematical analysis
Mechanics
Numerical stability
Physics
Two phase flow
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Summary: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.
ISSN:1070-6631
1089-7666
DOI:10.1063/5.0061638