A lattice Boltzmann model for the coupled cross-diffusion-fluid system

TL;DR

This paper introduces a lattice Boltzmann model for coupled cross-diffusion-fluid systems, accurately recovering macroscopic equations and effectively handling cross diffusion and convection effects, demonstrated through chemotaxis-fluid and double-diffusive convection applications.

Contribution

The paper presents a novel LB model that incorporates collision operators and source terms to simulate coupled cross-diffusion-fluid systems without special gradient treatments.

Findings

Successfully models chemotaxis-fluid system and double-diffusive convection.

Accurately reproduces steady-state and dynamic behaviors.

Results agree well with previous studies.

Abstract

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.