The Dilemma of Domain Decomposition Approaches in Fluid-Structure Interactions with Fully Enclosed Incompressible Fluids

Many popular non-overlapping domain decomposition approaches to fluid-structure interaction (FSI) problems fail to work for an interesting subset of FSI problems, the interaction of highly deformable structures with incompressible but fully enclosed fluids. This is particularly true for coupling approaches based on Dirichlet-Neumann substructuring, both for weak and strong coupling schemes. The breakdown of simulation can be attributed to a lack of knowledge transfer – e.g. of the incompressibility constraint to the structure – between the fields. Another explanation is the absence of any unconstrained outflow boundary at the fluid field, that is the fluid domain is entirely enclosed by Dirichlet boundary conditions. Inflating of a balloon with a prescribed inflow rate constitutes a simple problem of that kind. To overcome the dilemma inherent to partitioned or domain decomposition approaches in these cases a small augmentation is proposed that consists of introducing a volume constraint on the structural system of equations. Additionally the customary applied relaxation of the interface displacements has to be abandoned in favor of the relaxation of coupling forces. These modifications applied to a particular strongly-coupled Dirichlet-Neumann partitioning scheme result in an efficient and robust approach that exhibits only little additional numerical effort. A numerical example with large changes of fluid volume shows the capabilities of the proposed scheme.