Results and data used to validate the FIDF-IBM implementation against previous experimental/numerical data

A fast implicit direct-forcing immersed boundary method (FIDF-IBM) is introduced for the simulation of incompressible flows over arbitrarily moving solid structures. This method leverages the operator splitting approach of the pressure implicit with splitting of operators (PISO) algorithm to decouple the pressure, velocity, and boundary force in the solution process. This maintains the no-slip/no-penetration (ns/np) boundary constraint and enforces the divergence-free condition in a segregated manner in the solid and fluid domains, respectively. The proposed scheme produces a modified pressure Poisson equation (PPE) that includes the boundary force already satisfying the ns/np boundary constraint, allowing the usage of fast iterative PPE solvers. The term ``fast direct-forcing'' is achieved by coupling Lagrangian weight methods that enhance the reciprocity of the IBM-related linear operators with the IBM implicit formulation. Additionally, an appropriate boundary force inheritance from previous time-steps further boosts the performance of the implicit DF-IBM algorithm. The method's efficiency and capability are verified through different stationary and moving immersed boundary benchmark tests.