关键词: 平板, 热扩散, 有限元体积法, 有限差分法, 格子玻尔兹曼, 数值模拟

Abstract: When the traditional CFD method is used to solve the Navier⁃Stokes equation of incompressible flow, the pressure equation has an elliptical shape and cannot be solved, and the convergence is poor. Therefore, the traditional CFD method has certain limitations. In order to study the computational efficiency and accuracy of the lattice Boltzmann method compared with the traditional CFD method, taking the thermal diffusion problem of plates with constant temperature boundary as an example, the temperature field between the plates is solved by the finite element volume method, the finite difference method and the lattice Boltzmann method. By comparing the solution results and the number of normalized iteration steps, the feasibility, accuracy and efficiency of the lattice Boltzmann method are clarified. The results show that under the same physical model, the lattice Boltzmann method and the finite difference method are slightly better than the finite element volume method. The lattice Boltzmann method has the fastest solution speed and the least iteration steps, followed by the finite difference method, and the finite element volume method has slowest solution speed.

Key words: Plate, thermal diffusion, Finite element volume method, Finite difference method, Lattice Boltzmann, Numerical simulation