Comparison between two different decompositions for the solution of fluid-structure interaction problems

Abstract

Several types of decompositions and coupling algorithms can be used when solving a fluid-structure interaction problem in a partitioned way. In the case of Dirichlet- Neumann (DN) decomposition, the flow equations are solved with a Dirichlet boundary condition on the fluid-structure interface, while the structural equations are solved with a Neumann boundary condition on the interface. Robin-Neumann (RN) decomposition denotes a Robin boundary condition on the fluid side of the interface. It is well-known that Gauss-Seidel iteration is often unstable for strongly coupled problems with DN decomposition. Conversely, this coupling algorithm can have good convergence properties in combination with RN decomposition. The Interface Artificial Compressibility (IAC) method is one of the techniques to improve the convergence of the Gauss-Seidel iterations for cases with DN decomposition. In this paper, it is demonstrated that there is a common idea behind Gauss-Seidel iterations with RN decomposition and with DN decomposition plus IAC. Both approaches include a local, linear approximation for the structural equations into the flow equations. The numerical examples demonstrate that this approach is very suitable for the flow in flexible tubes, but that the application to other cases is not always straightforward.