Fixed-point fluid–structure interaction solvers with dynamic relaxation

Abstract

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.

Fluid–structure interaction in lower airways of CT‐based lung geometries

“…Satisfying the kinematic continuity leads to mass conservation at FSI , satisfying the dynamic continuity yields conservation of linear momentum and energy conservation finally requires to simultaneously satisfy both continuity equations. The algorithmic framework of the partitioned FSI analysis is discussed in detail elsewhere, Küttler and Wall [36], Mok and Wall [40] and Wall et al [44].…”

“…We use a partitioned approach that is based on a non-overlapping non-conforming iterative Dirichlet-Neumann substructuring scheme [36,40,44]. The coupling approach prescribes fluid velocities at the coupling interface of the fluid domain and applies the resulting forces to the coupling interface of the structural domain.…”

“…The coupling approach prescribes fluid velocities at the coupling interface of the fluid domain and applies the resulting forces to the coupling interface of the structural domain. Essential for robustness and efficiency of the coupling algorithm are the applied acceleration schemes for the iterative process [36,40]. For all numerical examples in this paper, the Aitken acceleration has been employed.…”

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

“…A detailed explanation of this coupling algorithm follows later. The convergence of Gauss-Seidel iterations is improved by Aitken relaxation [1] which uses a dynamically-adapted relaxation factor. Faster convergence is obtained with Newton methods [2] or in case of black-box solvers with the Interface Generalized Minimum Residual method [3] or with quasi-Newton methods like the interface block quasi-Newton method with approximate Jacobians from least-squares models (IBQN-LS) [4] and the interface quasi-Newton method with inverse Jacobian from a least-squares model (IQN-ILS) [5].…”

Assessment of the Fluid-Structure Interaction Capabilities for Aeronautical Applications of the Open-Source Solver Su2.

“…One common strategy to improve the convergence of the scheme is the use of high-order displacement predictors combined with the employment of relaxation techniques [35,40,43,44]. The definition of a fixed relaxation parameter ω generally results on a large number of iterations [43]; however, the use of the Aitken's ∆ 2 dynamic relaxation parameter [45], which has also been included in SU2, is a simple and efficient option [40,43,44] to improve the convergence of implicit schemes.…”