A kinetic theory-based lattice Boltzmann model for multicomponent systems with non-unitary molecular mass ratios

Resumo

The introduction of a non-unitary mass ratio for multicomponent systems is a difficult task in LBM discretization. In a kinetic model, the mean velocity of a particle is a function of the temperature and molecular mass. There are two strategies to carry out this information in the LBM framework: the Different Lattice Speeds (DLS) and the Same Lattice Speeds (SLS) methods (McCracken and Abraham, 2005). DLS models require either time or space interpolation, which are sources of errors. Alternatively, the SLS models available in the literature usually use ad hoc discretizations (Grunau et al., 1993; Reis and Philipps, 2007). These SLS models achieve high-density ratios by using a modified second-order equilibrium distribution allowing the manipulation of the number of particles at rest and the speed of sound. However, it has been proven that, when there is a density contrast, these second-order models are not able to correctly recover the linear momentum balance equation by themselves (Huang et al., 2013). Although third-order correction terms have been proposed in the literature, they follow the same ad hoc discretization proposition (Ba et al., 2016; Subhedar et al., 2022). The present work aims to demonstrate that the use of a kinetic theory-based LB model with prescribed abcissas quadrature of the Maxwell-Boltzmann equilibrium distribution (Philippi et al., 2006) is able to introduce a non-unitary mass ratio in LB simulations of multicomponent systems, carrying out the effects of mass to higher-order terms consistently. Using a full Hermitian representation of the D2Q9 LBE, including third- and fourth-order Hermite polynomials, this methodology was shown to be capable of achieving density ratios of up to 10⁶.