CENAERO 
The objective of this contribution is to deliver a second-order time-accurate solution for coupled aeroelastic problems. We compare in terms of accuracy, computational efficiency and numerical stability both loosely- and strongly-coupled staggered approaches. For this purpose the simulation of the transient aeroelastic responses of the AGARD Wing 445.6 and the Alenia SMJ regional jet are considered. 
Loosely- Versus Strongly-Coupled Staggered Solution Procedures for Large-Scale Unsteady Aeroelastic Problems
Large-scale nonlinear aeroelastic problems require the simultaneous application of computational fluid dynamics (CFD) and computational structural dynamics (CSD). Since each discipline has developed powerful specialized tools, a partitioned procedure is preferred for solving nonlinear aeroelastic problems. In the present research a in-house parallel threedimensional unstructured CFD solver is coupled through the MpCCI software [1] to the SAMCEF Mecano CSD code [2].
The objective of the CFD-Multiphysics Group at CENAERO is to deliver a second-order time-accurate solution for coupled aeroelastic problems. We compare in terms of accuracy, computational efficiency and numerical stability both loosely- and strongly-coupled staggered approaches. For this purpose the simulation of the transient aeroelastic responses of the AGARD Wing 445.6 and the Alenia SMJ regional jet are considered.
Used Approach (Software, Numerics, Modelling)
The time-integration of the coupled equations governing the nonlinear transient aeroelastic problem is performed with a partitioned solution procedure that can be described for one time-step as follows: (1) compute the fluid force and transfer it to the structure, (2) solve the structure subsystem, (3) transfer the displacement of the wet boundary of the structure to the fluid subsystem and update the position of the fluid mesh (with a structure analogy
method) accordingly, and (4) advance the fluid subsystem. If this procedures repeated until both the fluid and structure subsystems converge to an equilibrium, a staggered solution algorithm that is usually referred to as a strongly-coupled solution method is obtained. A loosely-coupled staggered solution algorithm is obtained if the above four-step procedure is only performed once.
In order to deliver a second-order time-accurate solution for coupled aeroelastic problems, both staggered procedures require that their individual time-integrators be second-order time-accurate. This can be achieved by selecting the ALE version [3] of the three-point backward difference scheme for time-integrating the fluid subsystem on moving meshes and the Newmark scheme for advancing in time the structure subsystem. Furthermore, the loosely-coupled staggered algorithm requires carefully designed structure displacement predictor and structure force corrector [4] in order to preserve the second-order time-accuracy of the individual fluid and structure time-integrators.
Expected Results
The objective of this contribution is to compare in terms of accuracy, computational efficiency and numerical stability both loosely- and strongly-coupled staggered approaches. For this purpose the simulation of the transient aeroelastic responses of the AGARD Wing 445.6 and the Alenia SMJ regional jet are considered.
Links to related Projects and Sites
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Cenaero
CFD-Multiphysics Group
Francois Thirifay
Rue des Frères Wright - Bâtiment EOLE, 1er étage
B-6041 Gosselies (Belgium)
www.cenaero.be
francois.thirifay@cenaero.be 
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