Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows

Stabilized explicit coupling for fluid–structure interaction using Nitsche's method

“…that only involve the solution of the fluid and the structure once (or just a few times) per time step (see [31,33,11] for instance), are known to give rise to numerical instabilities (first reported in [26], see also [24,30]). Theoretical explanations of this issue have been reported in [7] (see also [16]). In particular, in [16], it is argued that no explicit scheme can be constructed which would be unconditionally stable with respect to the fluid-structure density ratio.…”

“…A further analysis, considering different time discretization schemes, has been recently reported in [16]. In particular, the authors conclude that no sequentially staggered scheme can be constructed which would be unconditionally stable with respect to to the fluid-solid density ratio.…”

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

“…Such a block Gauss-Seidel iterative scheme provides strong coupling of the partitioned fluid and structure subproblems and, when implemented in conjunction with the implicit dual timestepping the scheme of the fluid solver and implicit Newmark/Newton-Raphson scheme of the structural solver, enables a large physical time step to be maintained. Depending upon the time step selected and/or the combined physical and geometrical parameters of the problem-certain classes of problem frequently encountered in biomedical modelling can be severely destabilized by the effects of the so-called added-mass phenomena [41,42]-subiterations may or may not be required at each time level for strong coupling to be achieved. In the examples presented here, matching discretizations have been generated at the interface to avoid the errors associated with data interpolation on highly non-matching discretizations during this implementation stage.…”

Stability analysis of Gauss–Seidel iterations in a partitioned simulation of fluid–structure interaction

“…It has been shown in several studies [8,7,9] that the instability of the coupling iterations within the time step has a physical cause. Consequently, the time discretization schemes are not expected to have much influence on the stability of the coupling iterations although they will influence the final result of the coupling iterations.…”

“…Förster et al [7] analyzed the effect of these parameters on algorithms without coupling iterations. Causin et al [8] studied algorithms with and without coupling iterations and derived the maximal relaxation factor that leads to convergence of coupling iterations as a function of the aforementioned parameters for a simplified model of blood flow in an artery and then validated the formulas with numerical experiments.…”