Résumé:
Solving fluid dynamics problems mainly rely on experimental methods and CFD (Computational Fluid Dynamics) based numerical simulations. However, in experimenta l methods it is difficult to simulate the physical problems in reality and there is also a high-cost
to the economy, while CFD simulation are sensitive about meshing a complicated structure. It is also time-consuming due to the billion degrees of freedom in relevant spatial-temporal flow
fields. Therefore, constructing a cost-effective model to settle fluid dynamics problems is of significant meaning. Physics-informed machine learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training a reliable model. This can be achieved by incorporating the residual of physics equations into the loss
function. Through minimizing the loss function, the network could approximate the solution.
In this report, we propose a physics-informed neural network (PINN) to solve fluid flows problems governed by the Navier-Stokes equations. We apply the proposed PINN to simulate steady incompressible laminar flows at low Reynolds numbers. The predicted velocity and pressure fields by the proposed PINN approach are also compared with the reference numerica l
solutions. Simulation results demonstrate great potential of the proposed PINN for fluid flow simulation with a high accuracy.
