On the Choice of Interface Parameters in Robin–Robin Loosely Coupled Schemes for Fluid–Structure Interaction

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.

Quasi-simultaneous coupling methods for partitioned problems in computational hemodynamics

“…The interaction law would nowadays be called an interface or transmission condition, but we like to stick to its original name as given more than four decades ago. It would be interesting to compare the outcome of the recent optimizations of the coefficients of Robin-Robin conditions [38] with the well-established physical models used as interaction law.…”

Partitioned and Monolithic Algorithms for the Numerical Solution of Cardiac Fluid-Structure Interaction

“…This typically yields stability issues: in particular, loosely coupled partitioned schemes (based on explicit time discretization of the whole FSI problem) may generate blowing-up solutions due to an incorrect energy balance [27]. Although in recent years stable loosely coupled partitioned schemes for hemodynamics were studied [18,24,25,40,49,50,52], here we focus on the two most traditional families of schemes that guarantee stability in hemodynamics:…”

“…The FSI numerical coupling schemes that have been proposed in the literature (see, e.g., [20,29,56,59,70]) can be roughly classified into partitioned loosely coupled (or explicit) schemes [18,24,25,40,49,50,52], partitioned fully coupled (or fixed-point, or implicit) schemes [14,15,27,69,70,76,78] and monolithic (or Newton-based) schemes [45,55,64,81,93,114,115]. The schemes differ significantly in their modularity and in the implementation effort that they require, and in terms of their performance [68,70].…”

A Robin-Neumann Scheme with Quasi-Newton Acceleration for Partitioned Fluid-Structure Interaction

“…Good choices of α RN balance out these two opposing trends, but are very difficult to determine a priori. Various highly recommendable works study the effect of the Robin parameter in detail, like Badia et al [19], Gerardo-Giorda et al [21], Cao et al [22,23], or Gigante and Vergara [24]. Analyzing simplified FSI problems, for example potential or inviscid flows interacting with linear beam or membrane models, they derive suggestions for choosing α RN , including both constant values and spatially varying expressions [23].…”

“…Unfortunately, however, the Robin-Neumann scheme also introduces new drawbacks. In particular, its performance is strongly governed by the Robin parameter that controls the weighting of Dirichlet and Neumann contributions; and although tuning this parameter has been studied for various simplified FSI problems [21][22][23][24], efficient choices are in general problem-dependent and difficult to find a priori.…”