Lattice Boltzmann study of the double-diffusive convection in porous media with Soret and Dufour effects

In this work, a coupled representative elementary volume scale lattice Boltzmann method (LBM) is developed to investigate double-diffusive convection in a porous cavity, taking into account Dufour and Soret effects. The governing equations comprise the incompressible Navier-Stokes equations and the coupled convection diffusion equations with cross diffusion terms, which pose challenges to the numerical methodology. To accurately handle the cross diffusion term, a comprehensive collision operator is introduced in the proposed LBM. By means of multi-scale Chapman-Enskog analysis, the coupled LBM successfully recovers the governing equations. Several benchmark double-diffusive convection problems are simulated to verify the reliability of the proposed LBM, showing good agreement with established data from previous research. Furthermore, the impacts of the Darcy number, Rayleigh number, and Soret and Dufour factors on heat and mass transfer rates are thoroughly examined, yielding calculations of average Nusselt number and Sherwood numbers under these dimensionless quantities. The numerical results underscore the capability of the developed LBM for simulating double-diffusive convection in porous media with Dufour and Soret effects.