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.

Automated summary

In this study, we propose a new semi-monolithic method for the simulation of fluid-structure interaction (FSI) problems. The method couples the pressure variables of the fluid domain with the displacement variables of the solid domain in a monolithic manner. Experimental results confirm that the proposed method can simulate FSI problems with strong added-mass effect and large deformation effectively. Compared to existing monolithic methods, the proposed method is faster and easier to precondition.