Generalized equilibria for color-gradient lattice Boltzmann model based on higher-order Hermite polynomials: A simplified implementation with central moments

Abstract

We propose generalized equilibria of a three-dimensional color-gradient lattice Boltzmann model for two-component two-phase flows using higher-order Hermite polynomials. Although the resulting equilibrium distribution function, which includes a sixth-order term on the velocity, is computationally cumbersome, its equilibrium central moments (CMs) are velocity-independent and have a simplified form. Numerical experiments show that our approach, as in Wen et al. [Phys. Rev. E 100, 023301 (2019)] who consider terms up to third order, improves the Galilean invariance compared to that of the conventional approach. Dynamic problems can be solved with high accuracy at a density ratio of 10; however, the accuracy is still limited to a density ratio of $1000$. For lower density ratios, the generalized equilibria benefit from the CM-based multiple-relaxation-time model, especially at very high Reynolds numbers, significantly improving the numerical stability.

23 pages, 8 figures

References in corpus (8)

• Consistent forcing scheme in the cascaded lattice Boltzmann method
• On the Three-dimensional Central Moment Lattice Boltzmann Method
• Multiphysics flow simulations using D3Q19 lattice Boltzmann methods based on central moments
• Lattice Boltzmann modeling and simulation of liquid jet breakup
• Cross-platform programming model for many-core lattice Boltzmann simulations
• Entropic multi-relaxation-time lattice Boltzmann model for large density ratio two-phase flows
• A quantitative comparison of physical accuracy and numerical stability of Lattice Boltzmann color gradient and pseudopotential multicomponent models for microfluidic applications
• Chromodynamic multi-relaxation time lattice Boltzmann scheme for fluids with density difference