Abstract
We consider two loosely coupled schemes for the solution of the fluid–structure interaction problem in the presence of large added mass effect. In particular, we introduce the Robin–Robin and Robin–Neumann explicit schemes where suitable interface conditions of Robin type are used. For the estimate of interface Robin parameters which guarantee stability of the numerical solution, we propose a new strategy based on the optimization of the reduction factor of the corresponding strongly coupled (implicit) scheme, by means of the optimized Schwarz method. To check the suitability of our proposals, we show numerical results both in an ideal cylindrical domain and in a real human carotid. Our results showed the effectiveness of our proposal for the calibration of interface parameters, which leads to stable results and shows how the explicit solution tends to the implicit one for decreasing values of the time discretization parameter.
Highlights
The numerical solution of fluid–structure interaction (FSI) problems is very challenging and many different strategies have been considered so far
Loosely coupled or explicit schemes for the numerical solution of the FSI problem are based on an overall explicit time discretization which leads to the solution of just one fluid and one structure problem per time step
For the numerical solution of problem (1b), (1c), (2a), (2b), (1e), and (1f), we introduce in Algorithm 1 the Explicit Robin–Robin loosely coupled scheme, obtained after time discretization and by prescribing condition (2a) as boundary condition for the fluid problem, with structure quantities taken from the previous time step, and condition (2b) to the structure problem
Summary
The numerical solution of fluid–structure interaction (FSI) problems is very challenging and many different strategies have been considered so far. Some studies introduced loosely coupled schemes for the FSI problem based on Robin interface conditions, obtained by considering linear combinations of the no-slip condition and action–reaction principle by means of suitable parameters [13,15,22,23,24,25,26,27,28]. In such works different proposals for the interface parameters were addressed with the aim of improving the stability properties when the added mass effect is relevant with respect to the explicit DN scheme. We verify the stability of the corresponding numerical solution in 3D FSI numerical experiments
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