We propose an interpolation-based lattice Boltzmann formulation that is applicable to non-conforming orthogonal meshes. This interpolation configuration allows the use of localized and directional refinement that reduces mesh sizes and makes them well adapted for solving flows in various configurations, including aerodynamic shapes in free streams. The novel aspect of the proposed method lies in the interpolation scheme selection algorithm, which uses local mesh topology for choosing a suitable combination of nodes and polynomial terms. The objective of this study consists of validating the scheme accuracy with well documented laminar incompressible flow test cases. The results demonstrate the capability of the proposed interpolation method to successfully solve closed and open flows with either straight or curved walls. Simulations for the flow over a NACA 0012 airfoil show that the aerodynamic coefficients are captured correctly using a mesh with large aspect ratio cells near the wall and in the airfoil wake.

我们提出了一种基于插值的格子玻尔兹曼公式，它适用于非一致正交网格。这种插值配置允许使用局部和定向细化，从而减小网格尺寸并使它们非常适合解决各种配置中的流动，包括自由流中的空气动力学形状。所提出方法的新颖之处在于插值方案选择算法，该算法使用局部网格拓扑来选择节点和多项式项的合适组合。本研究的目标包括使用有据可查的层流不可压缩流测试案例来验证方案的准确性。结果证明了所提出的插值方法能够成功解决具有直壁或弯曲壁的封闭和开放流动。