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

Degroote, Joris; Annerel, Sebastiaan; Vierendeels, Jan

doi:10.1016/j.compstruc.2009.09.003

Cited by 32 publications

(44 citation statements)

References 16 publications

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“…This observation is consistent with prior stability analyses [24,48,25]. Here, it is demonstrated that the adjoint simulation behaves in the same way.…”

Section: Stabilitysupporting

confidence: 79%

“…An approximation for the inverse of the Jacobian will lead to convergence of the coupling iterations if it contains the wave numbers in the interface displacement that are unstable during Gauss-Seidel iterations. For the flow in a one-dimensional flexible tube, it has been shown analytically that only a fraction of these wave numbers are unstable [25]. Other problems have shown similar behaviour.…”

Section: Coupling Iterationsmentioning

confidence: 68%

“…Figure 6 depicts the columns of the matrix V k for k = 5 in the first time step of a typical forward and adjoint simulation. It can be observed that the wave number of all columns is low for the forward simulation, as explained in [48,25,54]. Moreover, the columns in the adjoint simulation also have a relatively low wave number.…”

Section: Stabilitymentioning

confidence: 85%

“…However, it is well-understood that this coupling algorithm is unstable for fluid-structure interaction problems with an incompressible fluid and comparable density of the fluid and the structure [24,48,25]. Therefore, the interface quasi-Newton coupling algorithm with an approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS) is applied [22].…”

Section: Coupling Iterationsmentioning

confidence: 99%

“…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]. In comparisons consisting of several test cases, IQN-ILS requires fewer coupling iterations per time step than Aitken relaxation or Interface GMRES [22], and the computational cost ratio of a partitioned simulation with IQN-ILS to a monolithic simulation ranges from 0.56 to 3.16 [26].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Degroote

Hojjat

Stavropoulou

et al. 2012

Struct Multidisc Optim

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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.

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“…This observation is consistent with prior stability analyses [24,48,25]. Here, it is demonstrated that the adjoint simulation behaves in the same way.…”

Section: Stabilitysupporting

confidence: 79%

Section: Coupling Iterationsmentioning

confidence: 68%

Section: Stabilitymentioning

confidence: 85%

Section: Coupling Iterationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Degroote

Hojjat

Stavropoulou

et al. 2012

Struct Multidisc Optim

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View full text Add to dashboard Cite

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On stability and relaxation techniques for partitioned fluid‐structure interaction simulations

Lorentzon

Revstedt

2022

Engineering Reports

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The stability of relaxation techniques has been studied for strongly coupled fluid‐structure interaction (FSI) with application to a cantilever immersed in channel flow. The fluid is governed by Navier–Stokes equations for incompressible flow condition using turbulence modeling, and the solid is governed by the equation of motion with compressible material modeling. The applied kinematic description is Lagrangian for the solid and Eulerian for the fluid. The coupling of the state solvers is achieved by the Arbitrary Lagrange–Euler procedure, which involves a mesh motion solver, and the FSI procedure is stabilized by relaxation. It is shown that the stability can be related to the frequency shift caused by FSI, and they follow the same rate for the shape factor of the structure with an offset. The results correlate well to theoretical results and show that all relaxations fail for sufficient high‐frequency shift for given mesh resolution. We also propose a continuation technique to stabilize the solution near the instability region, which improves efficiency and can be integrated easily for the black‐box FSI solution procedure.

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Analysis of several subcycling schemes in partitioned simulations of a strongly coupled fluid‐structure interaction

Moerloose

Taelman

Segers

et al. 2018

Numerical Methods in Fluids

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Summary Fluid‐structure interaction (FSI) simulations are used extensively to calculate the vibration of structures subjected to an internal or external flow. In the case of partitioned FSI simulations, separate flow and structure solvers are used, which requires some kind of coupling between both. The time step in both solvers is typically taken the same, but this unnecessarily leads to long calculation times when the time step is small due to stability reasons in one of the two solvers. Subcycling, the procedure where the time step of one solver is chosen smaller than the time step used in the other solver, may reduce the computational cost of the FSI simulation. The subcycling procedure can be either explicit or implicit, the latter implying the use of coupling iterations in each time step. Contrary to explicit subcycling, no stability analyses of implicit subcycling schemes are found in the literature. In this paper, the temporal stability of the implicit subcycling procedure is investigated. The one‐dimensional flow in an elastic cylindrical tube is studied analytically. The results of this analysis are subsequently compared to a partitioned two‐dimensional axisymmetric FSI calculation with implicit coupling between the flow and structure solvers.

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

Cited by 32 publications

References 16 publications

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

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

On stability and relaxation techniques for partitioned fluid‐structure interaction simulations

Analysis of several subcycling schemes in partitioned simulations of a strongly coupled fluid‐structure interaction

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