Mesh optimization using an improved self-organizing mechanism

As more powerful computing hardware enables higher resolution simulations, a fast and flexible mesh optimization method is becoming increasingly indispensable for Computational Fluid Dynamics (CFD), which unfortunately remains a bottleneck in the current CFD workflows. In this paper, a novel mesh optimization method based on an improved self-organizing map (SOM) neural network is proposed to improve the accuracy and efficiency of numerical simulation while maintaining constant computational cost. During an improved competitive learning procedure in SOM, the node distribution with constant connectivity rapidly matches the characteristics of the flow field, which is predicted by a Multilayer Perceptron (MLP). Based on the local element volume and flow solution variations, annealing schemes for self-adaptation of important SOM parameters are designed to ensure the convergence of the proposed algorithm. Specially, a feasible region constraint and a smoothing constraint are embedded into the node movement to avoid mesh tangling and excessive mesh skewness, and make the transition between nodes gradual. The proposed approach is applicable to various types of meshes and is easy to implement without code intrusiveness. Comparative results on benchmark examples and typical CFD examples demonstrate that the proposed method attributes to both the improvement in the computational accuracy and efficiency. It exhibits the potential to be a flexible and promising tool for rapid mesh optimization in CFD and other engineering fields.