For use with the lattice Boltzmann method, the macroscopic boundary conditions need to be transformed into their mesoscopic counterparts. Commonly used mesoscopic boundary conditions use the equilibrium density function, which introduces undesirable artifacts into the numerical solution, especially near interfaces with other types of boundary conditions. In this work, several variants of the mesoscopic boundary conditions are summarized and numerically investigated by means of benchmark problems for the incompressible Navier-Stokes equations with known analytical solutions. To improve the numerical approximation of the velocity and pressure fields, moment-based boundary conditions are extended for the D3Q27 velocity model. Furthermore, the interpolated boundary conditions are improved. These newly developed boundary conditions are shown to produce results with a substantially smaller numerical error.

中文翻译：

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层流问题中格子玻尔兹曼法细观边界条件的研究


为了与格子玻尔兹曼方法一起使用，宏观边界条件需要转换为其介观对应条件。常用的介观边界条件使用平衡密度函数，这会在数值解中引入不需要的伪影，特别是在与其他类型边界条件的界面附近。在这项工作中，总结了介观边界条件的几种变体，并通过具有已知解析解的不可压缩纳维-斯托克斯方程的基准问题进行了数值研究。为了改进速度场和压力场的数值近似，针对 D3Q27 速度模型扩展了基于力矩的边界条件。此外，插值边界条件也得到了改善。这些新开发的边界条件被证明可以产生数值误差小得多的结果。