We present an alternative three-dimensional lattice Boltzmann collision operator consisting of a nonorthogonal basis of central moments. Our formulation is characterized by an intelligible derivation with a relatively simple and quite general implementation. It is successfully validated against several established, well-consolidated, well-defined benchmark problems, showing excellent properties in terms of accuracy and convergence. If compared to the adoption of the classical Bhatnagar-Gross-Krook operator, our model possesses superior stability.

The cascaded or central-moments-based lattice Boltzmann method (CM-LBM) is a robust alternative to the more conventional Bhatnagar-Gross-Krook-LBM for the simulation of high-Reynolds number flows. Unfortunately, its original formulation makes its extension to a broader range of physics quite difficult. In addition, it relies on CMs that are derived in an ad hoc manner, i.e., by mimicking those of the Maxwell-Boltzmann distribution to ensure their Galilean invariance a posteriori. This work aims at tackling both issues by deriving Galilean invariant CMs in a systematic and a priori manner, thanks to the Hermite polynomial expansion framework. More specifically, the proposed formalism fully takes advantage of the D3Q27 discretization by relying on the corresponding set of 27 Hermite polynomials (up to the sixth-order) for the derivation of both the discrete equilibrium state and the forcing term in an a priori manner. Furthermore, while keeping the numerical properties of the original CM-LBM, this work leads to a compact and simple algorithm, representing a universal methodology based on CMs and external forcing within the lattice Boltzmann framework. To support these statements, mathematical derivations and a comparative study with four other forcing schemes are provided. The universal nature of the proposed methodology is eventually proved through the simulation of single phase, multiphase (using both pseudopotential and color-gradient formulations), and magnetohydrodynamic flows.

In a recent work [A. De Rosis, R. Huang, and C. Coreixas, “Universal formulation of central-moments-based lattice Boltzmann method with external forcing for the simulation of multiphysics phenomena,” Phys. Fluids 31, 117102 (2019)], a multiple-relaxation-time lattice Boltzmann method (LBM) has been proposed by means of the D3Q27 discretization, where the collision stage is performed in the space of central moments (CMs). These quantities relax toward an elegant Galilean invariant equilibrium and can also include the effect of external accelerations. Here, we investigate the possibility to adopt a coarser lattice composed of 19 discrete velocities only. The consequences of such a choice are evaluated in terms of accuracy and stability through multiphysics benchmark problems based on single-, multi-phase, and magnetohydrodynamics flow simulations. In the end, it is shown that the reduction from 27 to 19 discrete velocities has only little impact on the accuracy and stability of the CM-LBM for moderate Reynolds number flows in the weakly compressible regime.

When boiling occurs in a liquid flow field, the phenomenon is known as forced-convection boiling. We numerically investigate such a boiling system on a cylinder in a flow at saturated conditions. To deal with the complicated liquid–vapor phase-change phenomenon, we develop a numerical scheme based on the pseudopotential lattice Boltzmann method (LBM). The collision stage is performed in the space of central moments (CMs) to enhance numerical stability for high Reynolds numbers. The adopted forcing scheme, consistent with the CM-based LBM, leads to a concise yet robust algorithm. Furthermore, additional terms required to ensure thermodynamic consistency are derived in a CM framework. The effectiveness of the present scheme is successfully tested against a series of boiling processes, including nucleation, growth, and departure of a vapor bubble for Reynolds numbers varying between 30 and 30 000. Our CM-based LBM can reproduce all the boiling regimes, i.e., nucleate boiling, transition boiling, and film boiling, without any artificial input such as initial vapor phase. We find that the typical boiling curve, also known as the Nukiyama curve, appears even though the focused system is not the pool boiling but the forced-convection system. Also, our simulations support experimental observations of intermittent direct solid–liquid contact even in the film-boiling regime. Finally, we provide quantitative comparison with the semi-empirical correlations for the forced-convection film boiling on a cylinder on the Nu-Ja diagram.

The cascaded lattice Boltzmann method decomposes the collision stage on a basis of central moments on which the equilibrium state is assumed equal to that of the continuous Maxwellian distribution. Such a relaxation process is usually considered as an assumption, which is then justified a posteriori by showing the enhanced Galilean invariance of the resultant algorithm. An alternative method is to relax central moments to the equilibrium state of the discrete second-order truncated distribution. In this paper, we demonstrate that relaxation to the continuous Maxwellian distribution is equivalent to the discrete counterpart if higher-order (up to sixth) Hermite polynomials are used to construct the equilibrium when the D3Q27 lattice velocity space is considered. Therefore, a theoretical a priori justification of the choice of the continuous distribution is formally provided for the first time.