标题： 用格子玻尔兹曼方法模拟各向异性Cahn-Hilliard方程 显示英文标题

标题： Modelling anisotropic Cahn-Hilliard equation with the lattice Boltzmann method

摘要： 各向异性Cahn-Hilliard方程常用于模拟纳米尺度晶体表面上的晶面金字塔的形成。 与各向同性Cahn-Hilliard模型相比，与强各向异性系数相关的非线性项在开发有效的数值方案方面带来了挑战。 在本工作中，我们提出了一种多松弛时间格子玻尔兹曼方法来求解各向异性Cahn-Hilliard方程。 为此，我们将原始方程重新表述为带有源项的非线性对流-扩散方程。 然后将修改后的平衡分布函数和源项引入计算中。 通过Chapman-Enskog分析，成功恢复了宏观控制方程。 为了验证所提出的方法，我们进行了数值模拟，包括液滴变形和旋节分解等案例。 这些结果与现有工作一致，证实了所提出方法的有效性。 此外，模拟结果表明该模型遵循能量耗散定律，进一步突显了所开发的格子玻尔兹曼方法的有效性。 显示英文摘要

摘要： The anisotropic Cahn-Hilliard equation is often used to model the formation of faceted pyramids on nanoscale crystal surfaces. In comparison to the isotropic Cahn-Hilliard model, the nonlinear terms associated with strong anisotropic coefficients present challenges for developing an effective numerical scheme. In this work, we propose a multiple-relaxation-time lattice Boltzmann method to solve the anisotropic Cahn-Hilliard equation. To this end, we reformulate the original equation into a nonlinear convection-diffusion equation with source terms. Then the modified equilibrium distribution function and source terms are incorporated into the computations. Through Chapman-Enskog analysis, it successfully recovers the macroscopic governing equation. To validate the proposed approach, we perform numerical simulations, including cases like droplet deformation and spinodal decomposition. These results consistent with available works, confirming the effectiveness of the proposed approach. Furthermore, the simulations demonstrate that the model adheres to the energy dissipation law, further highlighting the effectiveness of the developed lattice Boltzmann method.