Lattice Boltzmann equation for convection-diffusion flows with Neumann boundary condition.

Abstract

In this work, a lattice Boltzmann equation (LBE) is developed to convection-diffusion flows with Neumann boundary condition in complex geometry. The physical fluid domain together with the physical boundary is extended to a large domain similar to the fictitious domain method, and the original convection-diffusion equation (CDE) is reformulated for the large domain, where the Neumann boundary condition is naturally incorporated to CDE without separated explicit treatment. Based on this extended CDE for the large domain, the LBE solver is designed accordingly. Several classical simulations of pure thermal diffusion/natural convection between two concentrated cylinders, natural convection flow around a circular cylinder with constant heat flux in square cavity, and mixed convection flow in a square lid-driven cavity with a circular cylinder are carried out to validate the present method. Numerical results show that the predictions by present LBE agree well with theoretical or other results.