Universal formulation of central-moments-based lattice Boltzmann method with external forcing for the simulation of multiphysics phenomena

Abstract

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.