Stability analysis of different combinations of time-integration schemes in fluid-structure interaction simulations

Partitioned fluid-structure interaction simulations often use different time-integration schemes to discretize the different sub-problems. As such, the flow and structural equations can be solved with schemes that are particularly suited for each individual problem. However, using incompatible schemes, these simulations can encounter stability problems. In this research an analytical stability analysis is performed for a model of blood flow in an artery. The backward Euler scheme is used for the time discretization of the flow equations. For the structure two schemes are used: the BE scheme and the Hilber-Hughes-Taylor operator in which the numerical damping is controlled by a single parameter alpha. The influence of this parameter and some physiological parameters on the stability and the damping of the spurious modes is studied. According to this analysis, the combination of the BE and HHT scheme is stable, but the wave number, the numerical damping and the flow and structural density can affect the damping of the spurious modes considerably. To verify the analytical results, a numerical study is performed using nonlinear two-dimensional axisymmetric FSI simulations

Numerical analysis of the fluid-structure interaction in a membrane pump

In this research, the fluid-structure interaction in a recently developed membrane pump is analysed. The governing equations for the laminar flow and for the deformation of the membrane are solved with two separate codes, which are coupled with the quasi-Newton technique with an approximation for the inverse of the Jacobian from a least-squares model. After the description of the model and the solution techniques, a detailed analysis of the flow field, the deformation of the structure and the stress in the membrane is presented. An energetic analysis of the pump is performed, and the pump's efficiency is calculated

Fluid-structure interaction simulation of pulse propagation in arteries : numerical pitfalls and hemodynamic impact of a local stiffening

When simulating the propagation of a pressure pulse in arteries, the discretization parameters (i.e. the time step size and the grid size) need to be chosen carefully in order to avoid a decrease in amplitude of the traveling wave due to numerical dissipation. In this paper the effect of numerical dissipation is examined using a numerical fluid-structure interaction (FSI) model of the pulse propagation in an artery. More insight in the influence of the temporal and spatial resolution of the wave on the results of these simulations is gained using an analytical study in which the scalar linear one-dimensional transport equation is considered. Although this model does not take into account the full complexity of the problem under consideration, the results can be used as a guidance for the selection of the numerical parameters. Furthermore, this analysis illustrates the difference in accuracy that can be obtained using a second-order implicit time integration scheme instead of a first-order scheme. The results from the analytical and numerical studies are subsequently used to determine the settings necessary to obtain a grid and time step converged simulation of the wave propagation and reflection in a simplified model of an aorta with repaired aortic coarctation. This FSI model allows to study the hemodynamic impact of a stiff segment and demonstrates that the presence of a stiff segment has an important impact on a short pressure pulse, but has almost no influence on a physiological pressure pulse. This phenomenon is explained by analyzing the reflections induced by the stiff segment