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

TL;DR

This paper introduces a generalized equilibrium distribution for a 3D color-gradient lattice Boltzmann model using higher-order Hermite polynomials, enhancing Galilean invariance and stability for two-phase flow simulations.

Contribution

It presents a simplified implementation of higher-order Hermite polynomial-based equilibria with velocity-independent central moments, improving accuracy and stability in two-phase flow modeling.

Findings

Improved Galilean invariance over conventional models.

High accuracy at density ratio of 10 in dynamic problems.

Enhanced numerical stability at high Reynolds numbers.

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 $1\,000$. 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.