  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.
