  In this paper, we propose a lattice Boltzmann (LB) model for the generalized
coupled cross-diffusion-fluid system. Through the direct Taylor expansion
method, the proposed LB model can correctly recover the macroscopic equations.
The cross diffusion terms in the coupled system are modeled by introducing
additional collision operators, which can be used to avoid special treatments
for the gradient terms. In addition, the auxiliary source terms are constructed
properly such that the numerical diffusion caused by the convection can be
eliminated. We adopt the developed LB model to study two important systems,
i.e., the coupled chemotaxis-fluid system and the double-diffusive convection
system with Soret and Dufour effects. We first test the present LB model
through considering a steady-state case of coupled chemotaxis-fluid system,
then we analyze the influences of some physical parameters on the formation of
sinking plumes. Finally, the double-diffusive natural convection system with
Soret and Dufour effects is also studied, and the numerical results agree well
with some previous works.
