The Immersed Boundary Method (IBM) is a powerful computational framework for simulating fluid-structure interaction problems, particularly those involving complex, moving, and deforming geometries. Over the years, various IBM formulations have been developed. The classic IBM uses an elastic forcing for flexible boundaries, while the direct forcing IBM extends its application to rigid bodies. To accurately enforce the no-slip boundary condition, the velocity correction IBM was introduced as an implicit, often more accurate, alternative. More recently, advanced implementations have successfully combined the IBM with Navier-Stokes solvers and the Finite Element Method for robust simulations.
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