An interface Newton–Krylov solver for fluid–structure interaction

Bruggeman

Haelterman

et al. 2008

Computers & Structures

141

121

This paper focuses on the stability of the coupling iterations in the partitioned approach to fluid-structure interaction. Previous research has shown that the number of coupling iterations increases when the time step decreases or when the structure becomes more flexible which is explained here by Fourier error analysis of the unsteady, incompressible flow in an elastic tube. Substituting a linearized model of the structural solver into the flow solver makes the coupling more stable but is impracticable if the flow solver is a black box. Therefore the coupling iterations are stabilized by coupling with reduced-order models and Aitken underrelaxation.

Section: Introductionmentioning

confidence: 99%

Stability of a coupling technique for partitioned solvers in FSI applications

Bruggeman

Haelterman

et al. 2008

Computers & Structures

141

121

“…Algorithms without coupling iterations [23] and Gauss-Seidel iterations [1, 24,25] are mostly unstable in the case of strong interaction between the flow and the structure. However, quasi-Newton iterations [26,27] or Newton-Krylov techniques [28,29] can be used to solve such FSI problems in a partitioned way, even with black-box solvers. The main advantage of monolithic simulations is the stability of the solution process, whereas the most important benefit of the partitioned approach is that existing, mature and optimized codes for the subproblems can be reused.…”

Section: Introductionmentioning

confidence: 99%

Partitioned simulation of the interaction between an elastic structure and free surface flow

Computer Methods in Applied Mechanics and Engineering

Souto-Iglesias

Paepegem

et al. 2010

ARTICLE INFO ABSTRACT Keywords:Fluid-structure interaction Partitioned Free surface Volume-of-fluid Rolling tank Impact IQN-ILS Aitken relaxationCurrently, the interaction between free surface flow and an elastic structure is simulated with monolithic codes which calcúlate the deformation of the structure and the liquid-gas flow simultaneously. In this work, this interaction is calculated in a partitioned way with a sepárate flow solver and a sepárate structural solver using the interface quasi-Newton algorithm with approximation for the inverse of the Jacobian from a leastsquares model (IQN-ILS). The interaction between an elastic beam and a sloshing liquid in a rolling tank is calculated and the results agree well with experimental data. Subsequently, the impact of both a rigid cylinder and a flexible composite cylinder on a water surface is simulated to assess the effect of slamming on the components of certain wave-energy converters. The impact pressure on the bottom of the rigid cylinder is nearly twice as high as on the flexible cylinder, which emphasizes the need for fluid-structure interaction calculations in the design process of these wave-energy converters. For both the rolling tank simulations and the impact simulations, grid refinement is performed and the IQN-ILS algorithm requires the same number of iterations on each grid. The simulations on the coarse grid are also executed using Gauss-Seidel coupling iterations with Aitken relaxation which requires significantly more coupling iterations per time step.

“…programmes which calculate an output for a given input, but whose internal algorithms can neither be accessed nor modified. These methods include Gauss-Seidel iterations, Gauss-Seidel iterations with Aitken relaxation [18][19][20], interface GMRES [21] and interface quasi-Newton (IQN-ILS) iterations [22,23]. However, Gauss-Seidel iterations are often unstable if the ratio of the fluid density to the structure density is high, among other reasons [24,25].…”

Section: Introductionmentioning

confidence: 99%

Partitioned solution of an unsteady adjoint for strongly coupled fluid-structure interactions and application to parameter identification of a one-dimensional problem

Hojjat

Stavropoulou

et al. 2012

Struct Multidisc Optim

Unsteady fluid-structure interaction (FSI) simulations are generally time-consuming. Gradient-based methods are preferred to minimise the computational cost of parameter identification studies (and more in general optimisation) with a high number of parameters. However, calculating the cost function's gradient using finite differences becomes prohibitively expensive for a high number of parameters. Therefore, the adjoint equations of the unsteady FSI problem are solved to obtain this gradient at a cost almost independent of the number of parameters.Here, both the forward and the adjoint problems are solved in a partitioned way, which means that the flow equations and the structural equations are solved separately. The application of interest is the identification of the arterial wall's stiffness by comparing the motion of the arterial wall with a reference, possibly obtained from non-invasive imaging. Due to the strong interaction between the fluid and the structure, quasi-Newton coupling iterations are applied to stabilise the partitioned solution of both the forward and the adjoint problem.