Analysis of Dirichlet-Neumann and Neumann-Dirichlet Partitioned Procedures in Fluid-Structure Interaction Problems

Abstract

In the solution of fluid-structure interaction (FSI) problems, partitioned scheme is a modular algorithm in which the equations of fluid and structure are solved separately in an iterative manner through the exchange of suitable transmission conditions at the FS interface. Based on different simplified models of the fluid and the structure, in this work we derive a reduction factor at each iteration of the partitioned algorithm and then use it to illustrate in terms of convergence behavior that using structure normal stress as the boundary condition along the FS interface in the fluid solver and hence prescribing displacement boundary condition for the structure is actually better than the opposite approach. If we assume the structure dose not move, we can prove the geometric convergence of the iteration that enforces the continuities of velocities and normal stresses along the FS interface. Some aspects that arise in the context of the application of partitioned scheme to FSI problems are also highlighted.