A unified momentum equation approach for fluid-structure interaction (FSI) problems with stationary boundaries

A unified momentum equation approach based on velocity variables is presented for solving fluid-structure interaction problems. This approach has unique advantages in that the momentum equations of the solid and liquid domains are coupled so as to obtain a unified momentum approach allowing to treat the fluid and solid domains as a whole. This is accompanied by a description of spatial discretization over a staggered grid and a fully implicit temporal discretization. The resulting set of non-linear algebraic equations is solved by using a segregated approach, embedding a SIMPLE algorithm for the pressure calculation. The model has been applied to a test problem of flow between two parallel plates and the numerical results show favorable agreement with those obtained from ABAQUS. Results for other test problems are also presented to demonstrate the capabilities of the present model. Results show that this new method has several advantages over the previous methods such as consistent and uniform discretization, no interfacing algorithms, incorporation of the interface boundary conditions inherently into the formulation while maintaining the system stable by avoiding ill-conditioned systems.