Two new approaches for applying Neumann boundary condition in thermal lattice Boltzmann method

Abstract

In this article, two schemes have been presented for applying Neumann boundary condition in thermal lattice Boltzmann method. In Scheme 1, the heat flux is directly applied to the gradients of unknown distribution functions. In the following, using the results of this scheme, Scheme 2 is introduced having simpler structure than Scheme 1. Both schemes are independent of lattice arrangement. However, D2Q9 lattice arrangement is employed in this article. These two schemes are analyzed in several examples at different relaxation times, and second-order convergence accuracy is achieved for both schemes at the relaxation times. In contrast, other conventional methods, especially the ones which are based on passive scalar approach, give second-order convergence accuracy only at particular relaxation times. Moreover, it is shown that the two proposed schemes in this paper have better accuracy than the conventional method used for simulating adiabatic boundary condition, whereas they do not impose additional computational cost. In addition, the two schemes have also been applied on curved boundaries, and good agreement has been observed with exact solution.