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

摘要： 传统CFD方法在求解不可压缩流动Navier⁃Stokes方程时，压力方程具有椭圆形，无法推进求解，收敛性较差，因此传统CFD方法具有一定的局限性。对此研究格子玻尔兹曼方法与传统CFD方法的计算效率与准确性，以恒温边界的平板热扩散问题为例，分别运用有限元体积法、有限差分法及格子玻尔兹曼方法对平板间的温度场进行求解，通过对比求解结果及归一化迭代步数，明确格子玻尔兹曼方法计算的可行性、准确性与高效性。结果表明，相同物理模型条件下，格子玻尔兹曼方法和有限差分法的求解准确性要略优于有限元体积法；格子玻尔兹曼方法的求解速度最快，迭代步数最少，有限差分法、有限元体积法求解速度最慢。

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