Data-driven velocity reconstruction for immersed boundary methods

The Immersed Boundary Method (IBM) is widely used for incompressible flows with complex geometric boundaries. Among its variants, the direct forcing method is computationally and programmatically straightforward and effectively captures near-wall flow behavior. However, it struggles to maintain the divergence-free condition of the velocity field in unsteady incompressible flows. To address this issue, this paper proposes a data-driven velocity reconstruction approach for the immersed boundary method (DATA-I). By improving dataset construction and training methodologies, the method captures the nonlinear relationships of near-wall velocities, thereby preserving the divergence-free property in numerical simulations of incompressible flows. To validate the effectiveness of the proposed method, numerical simulations of two-dimensional flow around a circular cylinder at Reynolds numbers ranging from 20 to 500 were conducted. Additionally, the geometric generalization capability of the data-driven model was tested using flow cases around a square cylinder and a sharp wedge. In the steady flow past a circular cylinder, the method reduced divergence errors by 44.7% to 70.4% compared to traditional interpolation approaches. For unsteady cylinder flow, the error in the Strouhal number was controlled within 5%. This study offers a novel solution for accurately simulating near-wall flows in incompressible fluid dynamics using the IBM.