A stable time advancing scheme for solving fluid–structure interaction problem at small structural displacements

Partitioned subiterative coupling schemes for aeroelasticity using combined interface boundary condition method

“…Based on the code packages, Breuer et al (2012) developed a semi-implicit predictor-corrector coupling procedure for their FSI computations subjected to turbulent flows which were tackled by large eddy simulation. It is found that the stencils of Sy and Murea (2008), Murea and Sy (2009) and Breuer et al (2012) are analogous to that of Fernández, Gerbeau, and Grandmont (2007). All these papers have demonstrated that the semi-implicit coupling scheme brings a cheaper cost without compromising the quality of the obtained results, compared with the implicit coupling method.…”

“…A number of comprehensive reviews (Cebral and Löhner 1997;Felippa, Park, and Farhat 2001;Cebral and Löhner 2005;Wall et al 2006) are concerned with the explicit and implicit coupling approaches whereas a few brief overviews of the semi-implicit coupling approaches can be found in the introduction parts of Sy and Murea (2008), Sy (2009), Breuer et al (2012) and Fernández, Gerbeau, and Grandmont (2007). More recently, Hou, Wang, and Layton (2012) reviewed the representative methods for FSI computer modelling and presented some insightful discussion.…”

“…Providing a rigorous theoretical proof for the algorithm's stability, the authors have deduced that putting the explicit coupling substep outside the implicit coupling substep will not endanger the stability of the entire semi-implicit coupling scheme. Using the implicit Euler scheme for the fluid and the centred scheme for the structure, Sy and Murea (Sy and Murea 2008;Murea and Sy 2009) developed another semi-implicit coupling scheme for FSI where the interfacial consistency was guaranteed by solving an optimisation problem. The developed algorithm in Sy and Murea (2008) was shown to be unconditionally stable.…”

“…Using the implicit Euler scheme for the fluid and the centred scheme for the structure, Sy and Murea (Sy and Murea 2008;Murea and Sy 2009) developed another semi-implicit coupling scheme for FSI where the interfacial consistency was guaranteed by solving an optimisation problem. The developed algorithm in Sy and Murea (2008) was shown to be unconditionally stable. Based on the code packages, Breuer et al (2012) developed a semi-implicit predictor-corrector coupling procedure for their FSI computations subjected to turbulent flows which were tackled by large eddy simulation.…”

Partitioned formulation of internal and gravity waves interacting with flexible structures

“…Alternatively, one may employ a more mature FETI-DP or its allied methods [62], by solving for ðu f ; u s Þ first, then projecting out the frame displacement u b except the so-called cross points interface degrees of freedom, and the localized Lagrange multipliers are transforming the present localized Lagrange multipliers to the classical global Lagrange multipliers as detailed in [57]. There exist a plethora of allied methods labeled as semi-implicit algorithm (see, e.g., Sy and Murea [101]) that do need to satisfy the interface compatibility constraints at each time step. This may present fruitful avenue for further study.…”