When using the projection method(or fractional step method)to solve the incompressible Navier-Stokes equations,the projection step involves solving a large-scale pressure Poisson equation(PPE),which is computationally expensive and time-consuming.In this study,a machine learning based method is pro-posed to solve the large-scale PPE.An machine learning(ML)-block is used to completely or partially(if not sufficiently accurate)replace the traditional PPE iterative solver thus accelerating the solution of the incompressible Navier-Stokes equations.The ML-block is designed as a multi-scale graph neural net-work(GNN)framework,in which the original high-resolution graph corresponds to the discrete grids of the solution domain,graphs with the same resolution are connected by graph convolution operation,and graphs with different resolutions are connected by down/up prolongation operation.The well trained ML-block will act as a general-purpose PPE solver for a certain kind of flow problems.The proposed method is verified via solving two-dimensional Kolmogorov flows(Re=1000 and Re=5000)with different source terms.On the premise of achieving a specified high precision(ML-block partially replaces the tra-ditional iterative solver),the ML-block provides a better initial iteration value for the traditional iterative solver,which greatly reduces the number of iterations of the traditional iterative solver and speeds up the solution of the PPE.Numerical experiments show that the ML-block has great advantages in accelerating the solving of the Navier-Stokes equations while ensuring high accuracy.

Ruilin Chen;Xiaowei Jin;Hui Li

Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology,Harbin Institute of Technology,Harbin 150090,China;Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education,Harbin Institute of Technology,Harbin 150090,China;Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications,Harbin Institute of Technology(Shenzhen),Shenzhen 518055,China

力学快报（英文）

[1]Ruilin Chen;Xiaowei Jin;Hui Li-.A machine learning based solver for pressure Poisson equations)[J].力学快报（英文）,2022(05):315-321

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