A lattice Boltzmann source formulation for advection and anisotropic diffusion

In this paper, simulations of two-dimensional advection and anisotropic diffusion with the lattice Boltzmann formulation were performed. Based on revealing a source term into the convection-diffusion equation (CDE), this new LB formulation aims to propose an alternative method to solve problems involving heat transfer by advection and anisotropic diffusion. The new approach has the advantages of keeping the usual square lattice basis and avoiding any specific modification neither in relaxation-time expression nor in the equilibrium distributions functions. We present an efficient and intuitive LB formulation able to solve coupled heat transfer by advection and anisotropic diffusion. First, the model was validated by simulation of pure anisotropic diffusion. Then, validation is made by simulation of coupled advection and anisotropic diffusion. Comparisons were made with control volume method solutions, and excellent agreements were achieved.

Automated summary

In this paper, simulations using the lattice Boltzmann formulation were conducted to study the two-dimensional advection and anisotropic diffusion. A new LB formulation that introduces a source term into the convection-diffusion equation (CDE) was proposed as an alternative method for heat transfer problems. The new approach preserves the square lattice basis and does not require specific modifications in the relaxation-time expression or equilibrium distribution functions. The model was validated by simulating pure anisotropic diffusion and coupled advection and anisotropic diffusion, achieving excellent agreements with control volume method solutions.