A mesh optimization method using machine learning technique and variational mesh adaptation

Computational mesh is an important ingredient that affects the accuracy and efficiency of CFD numerical simulation. In light of the introduced large amount of computational costs for many adaptive mesh methods, moving mesh methods keep the number of nodes and topology of a mesh unchanged and do not increase CFD computational expense. As the state-of-the-art moving mesh method, the variational mesh adaptation approach has been introduced to CFD calculation. However, quickly estimating the flow field on the updated meshes during the iterative algorithm is challenging. A mesh optimization method, which embeds a machine learning regression model into the variational mesh adaptation, is proposed. The regression model captures the mapping between the initial mesh nodes and the flow field, so that the variational method could move mesh nodes iteratively by solving the mesh functional which is built from the estimated flow field on the updated mesh via the regression model. After the optimization, the density of the nodes in the high gradient area increases while the density in the low gradient area decreases. Benchmark examples are first used to verify the feasibility and effectiveness of the proposed method. And then we use the steady subsonic and transonic flows over cylinder and NACA0012 airfoil on unstructured triangular meshes to test our method. Results show that the proposed method significantly improves the accuracy of the local flow features on the adaptive meshes. Our work indicates that the proposed mesh optimization approach is promising for improving the accuracy and efficiency of CFD computation.