Semi-monolithic formulation based on a projection method for simulating fluid–structure interaction problems

For the simulation of fluid–structure interaction (FSI) problems, the monolithic method provides more robust convergence than the partitioned method but requires solving a larger matrix for a saddle-point problem that is difficult to precondition. We extend the existing semi-implicit method to propose a new semi-monolithic method for FSI simulation that uses a velocity boundary equation of a pressure Poisson equation so that only the pressure variables of the fluid domain are coupled with the displacement variables of the solid domain in a monolithic manner. The fluid domain is solved by employing a fractional four-step method for the incompressible Navier–Stokes equations based on an arbitrary Lagrangian–Eulerian (ALE) formulation, and the solid domain is solved by an updated Lagrangian method for simulating large nonlinear deformations. We applied the proposed method to 2D/3D benchmark problems with various time steps and density ratios, and the results confirmed that FSI problems with not only a strong added-mass effect but also a large deformation are simulated well. The proposed method is faster than the existing monolithic method because it solves a smaller matrix whose diagonal blocks are diagonally dominant matrices, which are much easier to precondition. © 2023 Elsevier Ltd