Physically Based Anisotropic Hexahedral Mesh Generation Method

Abstract Anisotropic meshes can better capture the anisotropic characteristics of the physical field, reduce the degree of freedom in solving, and improve the analysis accuracy. However, creating hexahedral meshes that are consistent with the results of physical analysis has proven to be challenging. To achieve this objective, this article proposes a physically based anisotropic hexahedral mesh generation method. This method directly generates meshes with element anisotropy based on the results of physical analysis. First, the initial Riemannian metric field of the model is obtained through posterior error analysis on a tetrahedral mesh. Then, an energy equation is constructed and solved for the optimized Riemannian metric field. Then, the model is deformed based on the Riemannian metric field to achieve metric space conversion, resulting in the transformation of the anisotropic mesh generation problem into the isotropic mesh generation problem. Finally, a uniform hexahedral mesh is generated for the deformation model using polycube-based method, and the anisotropic hexahedral mesh of the original model is obtained through inverse mapping and quality improvement. Experimental results demonstrate that, compared with isotropic hexahedral meshes at the same granularity, the anisotropic hexahedral mesh generated by the proposed method can reduce the maximum analysis error and achieve higher solution accuracy.