단순격자볼츠만법에서 거시적변수들을 기반으로 한 대류경계조건 적용

Abstract

Recently, researchers have developed simple lattice Boltzmann method without evolution of distribution functions. The method has an advantage that physical boundary conditions can be implemented directly. Taking the advantage, we implement a convection boundary scheme to the simple lattice Boltzmann method. This boundary scheme is derived from an assumption that the convection heat flux is equal to the conduction heat flux. Then, the heat transfer coefficient can be expressed by the thermal conductivity. Using the coefficients, the wall temperature is set directly on the boundary condition of simple lattice Boltzmann method unlike convectional lattice Boltzmann method. For verifications and validations, we apply our scheme to three cases in a row. First of all, we compute a natural convection in a square cavity for validation of simple lattice Boltzmann method. Secondly, the convection boundary scheme is applied to steady one-dimension heat conduction on a solid. Lastly, we simulate a square cavity with the convection boundary scheme. In this case, we assume that the boundary is thin. Our result is compared with commercial solver, FLUENT. The results show that the convection boundary scheme used in this study can be applied to the simple lattice Boltzmann method.