Fluid structure interaction problem is one of ship hydrodynamics and hydraulic engineering applications of free surface flow^[1]. This issue involves the interaction between fluid and structure that is a strong nonlinear problem, especially for moving structures or deformable solid. In traditional one-way coupling or two-way partitioned coupling scheme, the velocity of solid is used to prescribe velocity boundary conditions on the fluid, and the fluid to provide force boundary conditions on the solid. In the special case for static solid or prescribed velocity rigid, there is no need to update the state of solid body in the next step^[2,3]. But for elastic and unconstrained rigid body, the pressure from the fluid domain can be both stiff and noisy as compared to the velocity field^[4]. It’s difficult to accurately evaluate the interaction from the fluid flow..

In this paper, we estimate the acting force through a new variational scheme of pressure project that can avoid the noisy of contact force from the traditional incompressible material point method. The key idea of this FSI scheme is based on variational form of pressure projection introduced by Batty^[5]. In each time step, the system including fluid and solid are treated as a perfectly inelastic process with an assumption that the fluid is incompressible. We can get a minimization form of the pressure projection. The most advantage of this method is that the complex solid boundaries can be handled automatically and the solid can be solved with other numerical method such as FE method. Our new scheme takes full advantages of incompressible material point method in solving fluid and finite element method in solving deformable structure. Finally, the proposed method is verified by various test examples such as water entry, dam break with interacting with a rubber gate which shows that the proposed FSI scheme of incompressible material point method coupling with finite element method is a powerful tool for solving fluid structure interaction problems.

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Keywords: Fluid structure interaction; Incompressible material point method; Pressure projection.