A monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure Poisson equation

This paper describes a new monolithic approach based on the fluid pressure Poisson equation (PPE) to solve an interaction problem of incompressible viscous fluid and an elastic body. The PPE is derived so as to be consistent with the coupled equation system for the fluid-structure interaction (FSI). Based on this approach, we develop two kinds of efficient monolithic methods. In both methods, the fluid pressure is derived implicitly so as to satisfy the incompressibility constraint, and all other unknown variables are derived fully explicitly or partially explicitly. The coefficient matrix of the PPE for the FSI becomes symmetric and positive definite and its condition is insensitive to inhomogeneity of material properties. The arbitrary Lagrangian–Eulerian (ALE) method is employed for the fluid part in order to take into account the deformable fluid-structure interface. To demonstrate fundamental performances of the proposed approach, the developed two monolithic methods are applied to evaluate the added mass and the added damping of a circular cylinder as well as to simulate the vibration of a rectangular cylinder induced by vortex shedding