Mesh adaptation for unsteady flow field based on machine learning

Existing grid adaptation methods for numerical simulation of unsteady flow fields usually perform grid adjustment every time step, which increases the computational complexity and the possibility of accuracy loss. In view of this, based on the DG finite element method, an MMPDE mesh adaptation method combined with BPNN is proposed for intelligent mesh optimization of unsteady flow fields. The method first uses the DG finite element method to solve the unsteady N-S equation and obtain the statistical grid discontinuity. Using the initial grid and grid discontinuity to train the BPNN regression model, the discontinuity value of any node at any position can be predicted. The variational method, MMPDE, is selected to move grid nodes to conform to the distribution of discontinuities. Finally, the Laplacian grid smoothing method improves the grid quality. The feasibility of the method is verified by cases of unsteady flow fields around cylinders. The calculation results show that the method can complete the one-time adaptive adjustment of the grid without changing the grid topology and the number of nodes, which can significantly improve the accuracy and efficiency of numerical simulations for unsteady flow fields.