Numerical simulation of Neumann boundary condition in the thermal lattice Boltzmann model

Abstract

In this paper, a bilinear interpolation finite-difference scheme is proposed to handle the Neumann boundary condition with nonequilibrium extrapolation method in the thermal lattice Boltzmann model. The temperature value at the boundary point is obtained by the finite-difference approximation, and then used to determine the wall temperature via an extrapolation. Our method can deal with the boundaries with complex geometries, motions and gradient boundary conditions. Several simulations are performed to examine the capacity of this proposed boundary method. The numerical results agree well with the analytical solutions. When compared with a representative boundary method, an improved performance is observed. The results also show that the proposed scheme together with nonequilibrium extrapolation method has second-order accuracy.