StruMNet: A Structural Mesh Generation Method Integrating Neural Networks and Partial Differential Equations

Mesh generation is a crucial step in the preprocessing phase of computational fluid dynamics (CFD) and plays a vital role in the overall CFD numerical simulation process. To further enhance the efficiency and intelligence of mesh generation, we propose StruMNet, a structured mesh generation method that integrates neural networks with partial differential equations. This method takes the boundaries of the computational domain and internal sampling points as inputs to establish a neural network model combined with partial differential equations for mesh generation. The loss function incorporates both control equation loss and geometric boundary constraint loss as optimization objectives. Additionally, the method introduces an adaptive weighting strategy for the loss function and a point-weighting mechanism to enhance mesh quality and fitting capabilities, especially at complex boundaries. Once trained, StruMNet can predict mesh points based on given boundary shapes. Experimental results show that StruMNet outperforms the physics-informed neural networks method and the MGNet method in terms of mesh quality across various geometries and improves mesh generation efficiency by three orders of magnitude compared to traditional methods, ultimately enabling the rapid generation of structured meshes.