Some numerical aspects for the coupling process of a discrete non-linear aeroelastic system are presented. The objective of this paper is two-fold: first, a consistent time-integration method of the whole coupled system is developed and the robustness is shown. Second, several data transfer methods — conservative interpolation, Galerkin-based transfer, dual-Lagrange-based transfer, and Sobolev-norm-based transfer — are employed and the importance of an accurate transfer scheme is demonstrated. Numerical results obtained from simulations of an oscillating one-dimensional plate in a transonic flow and a three-dimensional wing example serve as a typical benchmark problem to show the applicability of the presented concepts and the importance on the behaviour of an aeroelastic system.
BendiksenO. O.Modern developments in computational aeroelasticity. Proc. Instn Mech. Engrs, Part G: J. Aerospace Engineering, 2004, 218, 157–177.
2.
FriedmannP. P.Renaissance of aeroelasticity and its future. J. Aircr., 1999, 36(1), 105–121.
3.
FarhatC.LesoinneM.Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Comput. Methods Appl. Mech. Eng., 2000, 182, 499–515.
UngerR.HauptM. C.HorstP.Application of Lagrange multipliers for coupled problems in fluid and structural interactions. Comput. Struct., 2007, 85, 796–809.
6.
MassjungR.Numerical schemes and well-posedness in nonlinear aeroelasticity. PhD Thesis, Faculty of Mathematics, Computer Science and Natural Sciences, RWTH Aachen, 2000.
7.
GordnierR. E.MelvilleR. B.Transonic flutter simulations using an implicit aeroelastic solver. J. Aircr., 2000, 37(5), 872–879.
8.
PipernoS.Explicit/implicit fluid/structure staggered procedures with a structural predictor and fluid subcycling for 2D inviscid aeroelastic simulations. Int. J. Numer. Methods Fluids, 1997, 25(10), 1207–1226.
9.
BatheK. J.Finite element procedures, 1996 (Prentice Hall, Englewood Cliffs, NJ).
10.
HughesT. J. R.The finite element method: linear static and dynamic finite element analysis, 1987 (Prentice Hall, Englewood Cliffs, NJ).
11.
BlazekJ.Computational fluid dynamics: principles and applications, 2007 (Elsevier, Amsterdam).
12.
FerzigerH. J.PeriéM.Computational methods for fluid dynamics, 2002 (Springer, Berlin).
13.
JamesonA.Time dependent calculations using multigrid with application to unsteady flows past airfoils and wings. AIAA-paper 91-0596, 1991.
14.
ParkK. C.FelippaC. A.A variational principle for the formulation of partitioned structural systems. Int. J. Numer. Methods Eng., 2000, 47, 395–418.
15.
CebralJ. R.LöhnerR.Conservative load projection and tracking for fluid-structure problems. AIAA J., 1997, 35(4), 687–692.
16.
JiaoX. M.HeathM. T.Common-refinement-based data transfer between non-matching meshes in multi-physics simulations. Int. J. Numer. Methods Eng., 2004, 61(14), 2402–2427.
17.
FlemischB.PusoM. A.WohlmuthB. I.A new dual mortar method for curved interfaces: 2D elasticity. Int. J. Numer. Methods Eng., 2005, 63(6), 813–832.
18.
El-AbbasiN.BatheK. J.Stability and patch test performance of contact discretizations and a new solution algorithm. Comput. Struct., 2001, 79(16), 1473–1486.
19.
PusoM. A.A 3D mortar method for solid mechanics. Int. J. Numer. Methods Eng., 2004, 59(3), 315–336.
20.
YatesE. C.LandN. S.FoughnerJ. T.Measured and calculated subsonic and transonic flutter characteristics of a 45° sweptback wing platform in air and freon-12 in the Langley transonic dynamics tunnel. Technical report. NASA, 1963, D-1616.
21.
Lee-RauschE. M.BatinaJ. T.Calculation of AGARD wing 445.6 flutter using Navier-Stokes aerodynamics. AIAA-paper 93-3476, 1993.
22.
GuptaK. K.Development of a finite element aeroelastic analysis capability. J. Aircr., 1996, 33(5), 995–1002.
23.
IronsB. M.TuckR. C.A version of the Aitken accelarator for computer implementation. Int. J. Numer. Methods Eng., 1969, 1, 275–277.
24.
UngerR.HauptM. C.HorstP.Comparison of iterative solution procedures for fluid and structural interaction problems using two- and three-field approaches. In Computational methods for coupled problems in science and engineering II - coupled problems (Eds PapadrakakisM.OñateE.SchreflerB.), 2007 (International Center for Numerical Methods in Engineering (CIMNE), Barcelona).
25.
GeroldT.GalleM.FriedrichO.EvansJ.Calculation of complex three-dimensional configurations employing the DLR-TAU code. AIAA-paper 97-0167, 1997.
26.
YatesE. C.AGARD standard aeroelastic configuration for dynamic response, candidate configuration I - wing 445.6 Technical report. NASA TM-100492, 1987.
27.
ChenX.ZhaG.YangM.Numerical simulation of 3-d wing flutter with fully coupled fluid-structure interaction approach. AIAA-paper 2006-0697, 2006.
28.
WoodgateM. A.BadcockK. J.Fast prediction of transonic aeroelastic stability and limit cycles. AIAA J., 2007, 45(6), 1370–1381.
