Immersed boundary method combined with proper generalized decomposition for simulation of a flexible filament in a viscous incompressible flow

In this paper, a combination of the Proper Generalized Decomposition (PGD) with the Immersed Boundary method (IBM) for solving fluid-filament interaction problem is proposed. In this combination, a forcing term constructed by the IBM is introduced to Navier-Stokes equations to handle the influence of the filament on the fluid flow. The PGD is applied to solve the Poission's equation to find the fluid pressure distribution for each time step. The numerical results are compared with those by previous publications to illustrate the robustness and effectiveness of the proposed method.