AbstractThe paper analysis the incorporation of the source term in the advection-diffusion equation for the BGK Lattice Boltzmann Method (LBM). The problem is the coupled energy and species conservation equations with the Soret term. The problem is extremely important for people using LBM in simulating multi-physics, because multi-physics effect added as a source term to LB. A Few BGK LBM models were used, namely D1Q2, D1Q3, D2Q4 and D2Q5 to solve advection-diffusion-reaction problems. The aim of this work is to demonstrate that the lattice Boltzmann method is able to simulate Soret effect, where the source term is the curvature of the temperature field. Theoretical analysis of the force inclusion is also presented in the paper. To insure that the predictions are correct and consistent with the traditional methods, comparison of LBM predictions with the finite difference method (FVM) predictions were illustrated. Also, the results show that prediction of D1Q2 may suffer from oscillation.
Lattice Boltzmann method for the fractional advection-diffusion equation
