Interface tracking characteristics of color-gradient lattice Boltzmann model for immiscible fluids

• Published in: Physical review. E 2020-01, Vol.101 (1-1), p.013313-013313, Article 013313
• Main Authors: Subhedar, A, Reiter, A, Selzer, M, Varnik, F, Nestler, B
• Format: Article
• Language: English
• ISSN: 2470-0045; 2470-0053
• DOI: 10.1103/PhysRevE.101.013313

We study the interface tracking characteristics of a color-gradient-based lattice Boltzmann model for immiscible flows. Investigation of the local density change in one of the fluid phases, via a Taylor series expansion of the recursive lattice Boltzmann equation, leads to the evolution equation of the order parameter that differentiates the fluids. It turns out that this interface evolution follows a conservative Allen-Cahn equation with a mobility which is independent of the fluid viscosities and surface tension. The mobility of the interface, which solely depends upon lattice speed of sound, can have a crucial effect on the physical dynamics of the interface. Further, we find that, when the equivalent lattice weights inside the segregation operator are modified, the resulting differential operators have a discretization error that is anisotropic to the leading order. As a consequence, the discretization errors in the segregation operator, which ensures a finite interface width, can act as a source of the spurious currents. These findings are supported with the help of numerical simulations.