Optimal surface-tension isotropy in the Rothman-Keller color-gradient lattice Boltzmann method for multiphase flow

Area of Science:

• Computational fluid dynamics
• Multiphase flow simulation
• Applied mathematics

Background:

• The Rothman-Keller color-gradient (CG) lattice Boltzmann method is widely used for two-phase flow simulations, handling large viscosity contrasts and interfacial tensions.
• Standard CG calculations suffer from finite-difference errors, leading to interfacial tension anisotropy and spurious currents, particularly at high curvatures.
• Existing methods struggle with accuracy for interfaces with small radii of curvature, impacting the simulation of phenomena like pinchouts.

Purpose of the Study:

• To investigate the accuracy of standard color-gradient calculations for fluid interfaces with varying radii of curvature.
• To develop a more accurate, second-order color-gradient calculation to minimize anisotropy.
• To demonstrate the impact of improved CG calculations on simulating complex multiphase flow phenomena.

Main Methods:

• Analysis of standard CG calculation accuracy for interfaces with different radii of curvature.
• Derivation of a second-order accurate CG method by optimizing weights for diagonal nearest neighbors.
• Comparison of simulation results using standard and improved CG methods, focusing on anisotropy reduction and phenomenon capture.

Main Results:

• Standard CG calculations exhibit significant anisotropy (up to 7%) for high-curvature interfaces, such as pinchouts.
• The derived second-order accurate CG method, with optimized weights, reduces anisotropy to less than a percent.
• Optimal weights yield over a factor of 10 decrease in anisotropy and up to a factor of 15 decrease in mean anisotropic error compared to standard and previous methods.

Conclusions:

• The developed second-order accurate CG method significantly improves the isotropy of interfacial tension in lattice Boltzmann simulations.
• This enhancement allows for more reliable simulations of pore-scale processes like viscous fingering and droplet formation.
• Improved CG calculations enable the accurate capture of phenomena, such as droplet formation during fluid invasion, not observed with standard methods.