A Direct-Forcing Immersed Boundary Method for Incompressible Flows Based on Physics-Informed Neural Network

The application of physics-informed neural networks (PINNs) to computational fluid dynamics simulations has recently attracted tremendous attention. In the simulations of PINNs, the collocation points are required to conform to the fluid–solid interface on which no-slip boundary condition is enforced. Here, a novel PINN that incorporates the direct-forcing immersed boundary (IB) method is developed. In the proposed IB-PINN, the boundary conforming requirement in arranging the collocation points is eliminated. Instead, velocity penalties at some marker points are added to the loss function to enforce no-slip condition at the fluid–solid interface. In addition, force penalties at some collocation points are also added to the loss function to ensure compact distribution of the volume force. The effectiveness of IB-PINN in solving incompressible Navier–Stokes equations is demonstrated through the simulation of laminar flow past a circular cylinder that is placed in a channel. The solution obtained using the IB-PINN is compared with two reference solutions obtained using a conventional mesh-based IB method and an ordinary body-fitted grid method. The comparison indicates that the three solutions are in excellent agreement with each other. The influences of some parameters, such as weights for different loss components, numbers of collocation and marker points, hyperparameters in the neural network, etc., on the performance of IB-PINN are also studied. In addition, a transfer learning experiment is conducted on solving Navier–Stokes equations with different Reynolds numbers.