A fixed-point fluid-structure interaction (FSI) solver with dynamic relaxation is revisited. New developments and insights gained in recent years motivated us to present an FSI solver with simplicity and robustness in a wide range of applications. Particular emphasis is placed on the calculation of the relaxation parameter by both Aitken's ∆ 2 method and the method of steepest descent. These methods have shown to be crucial ingredients for efficient FSI simulations.

SUMMARYThe coupling of flexible structures to incompressible fluids draws a lot of attention during the last decade. Many different solution schemes have been proposed. In this contribution, we concentrate on the strong coupling fluid-structure interaction by means of monolithic solution schemes. Therein, a Newton-Krylov method is applied to the monolithic set of nonlinear equations. Such schemes require good preconditioning to be efficient. We propose two preconditioners that apply algebraic multigrid techniques to the entire fluid-structure interaction system of equations. The first is based on a standard block Gauss-Seidel approach, where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem. The second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields. The resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance.

SUMMARYThe coupling of lightweight and often thin-walled structures to fluids in an incompressible regime is a recurring theme in biomechanics. There are many fluid-structure interaction (FSI) solution schemes to address these kinds of problem, each one with its costs and benefits. Here, we attempt a comparison of the most important FSI schemes in the context of biomechanical problems, that is a comparison of different fixed-point schemes and a block preconditioned monolithic scheme. The emphasis of this study is on the numerical behavior of these FSI schemes to gain an understanding of their effectiveness in comparison with each other. To this end a simplified benchmark problem is studied to show its applicability for more involved biomechanical problems. Two such examples with patient-specific geometries are also discussed. The monolithic scheme proved to be much more efficient than the partitioned schemes in biomechanical problems.

In a subset of fluid-structure interaction (FSI) problems of incompressible flow and highly deformable structures all popular partitioned approaches fail to work. This also holds for recently quite popular strong coupling approaches based on Dirichlet-Neumann substructuring. This subset can be described as the special case where the fluid domain is entirely enclosed by Dirichlet boundary conditions, i.e. prescribed velocities. A vivid simple example would be a balloon with prescribed inflow rate. In such cases the incompressibility of the fluid cannot be satisfied during standard alternating FSI iterations as the deformation of the coupling surface is determined by the structural displacement that usually does not know about the current constraint on the fluid field. By analyzing this deficiency of the partitioned algorithm a small augmentation is proposed which allows to overcome the dilemma of incompressibility and fixed boundary velocities by introducing the volume constraint on the structural system of equations. In contrast to the original accelerated strong coupling partitioned method, the relaxation which ensures convergence of the iteration over the different fields has now to be performed on the coupling forces rather than on the displacements. In addition, two alternative approaches are discussed for the solution of the dilemma. The capability of the proposed method to deal with largely changing volumes of enclosed fluid is demonstrated by means of numerical examples.

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