Immersed boundary method-incorporated physics-informed neural network for simulation of incompressible flows around immersed objects

In this work, an immersed boundary method-incorporated physics informed neural network (IBM-PINN) is proposed to simulate steady incompressible flows around immersed objects. The conventional physics-informed neural network (PINN) can work without using a mesh, but it still requires arranging suitable collocation points within the computational domain. This task becomes particularly challenging in scenarios involving flows around complex geometry. By introducing the concept of the immersed boundary method (IBM) and using the incompressible N-S equations with volume force as the governing equation, the proposed IBM-PINN can simulate flows around complex geometry using only a simple distribution of collocation points. Furthermore, recognizing that the use of numerical algorithms instead of the AD method for calculating the derivatives of PINN results in higher efficiency and accuracy, we apply the finite difference (FD) method to calculate the derivative terms of IBM-PINN. The performance of the proposed IBM-PINN is evaluated by some benchmark problems, including flows around a cylinder and a NACA0012 airfoil. The results demonstrate excellent agreement between IBM-PINN solutions and IBM data. Additionally, we enhance the training of IBM-PINN by incorporating some internal samples for more complex flows such as the flow around the NACA0012 airfoil with an angle of attack (AoA) of 7° and the flow around the tandem twin circular cylinders. The numerical results reveal that the IBM-PINN can yield reasonable results with only a limited amount of internal samples.