An improved implicit direct-forcing immersed boundary method (DF-IBM) around arbitrarily moving rigid structures

An improved implicit direct-forcing immersed boundary method (DF-IBM) is presented for simulating incompressible flows around complex rigid structures undergoing arbitrary motion. The current approach harnesses the pressure implicit with splitting of operators algorithm to handle the fluid–solid system's dual constraints in a segregated manner. As a result, the divergence-free condition is preserved throughout the Eulerian domain, and the no-slip velocity boundary condition is exactly enforced on the immersed boundary. A new pressure Poisson equation (PPE) is derived, incorporating the boundary force where the no-slip condition is already met, enabling the use of fast iterative PPE solvers without modifications. The improvement involves integrating Lagrangian weight methods having better reciprocity over the IBM-related linear operators with the implicit formulation. An additional force initialization scheme is introduced to further boost the algorithm's performance. The method's accuracy, efficiency, and capability are verified through various stationary and moving immersed boundary cases. The results are validated against experimental and numerical data from the literature. The proposed improvements seamlessly integrate into existing incompressible fluid solvers with minimal adjustments to the original system equations, highlighting their ease of implementation.