A unified approach for the solution of fluid-solid interaction problems with hyperelastic deformation in internal flows

In the single domain method for solving fluid–solid interaction (FSI) problems, a unified formulation is used for the entire computational domain. In such monolithic FSI solvers, all of the governing equations are solved simultaneously. In the present study, the single domain method is further extended to an interface-tracking FSI solver which accounts for mesh movement via an Arbitrary Lagrangian–Eulerian (ALE) description of the governing equations. The focus is on internal flow problems with large deformation. Pressure and velocity are selected as the dependent variables for both solid and fluid parts of the computational domain. A distinguishing feature of the proposed method is that the governing equations at the interface are discretized in a conservative manner. Interfacial boundary conditions are enforced via a pressure–velocity splitting method to convert the kinematic and dynamic conditions at the interface into pressure–velocity relations. A PISO-like procedure is used to solve the discretized equations. In order to evaluate the proposed solver, strongly-coupled FSI benchmark test cases are employed. The performance of the proposed method and computational results are also compared with those obtained by a conventional partitioned solver. The results show that the proposed solver provides more accurate results on a coarser mesh compared to the benchmark solutions. The proposed method is also capable of solving strongly coupled problems for which the partitioned solver fails to converge.