## Partitioned procedures for the transient solution of coupled aeroelastic problems. I: Model problem, theory and two-dimensional application.(English)Zbl 1067.74521

Summary: In order to predict the dynamic response of a flexible structure in a fluid flow, the equations of motion of the structure and the fluid must be solved simultaneously. In this paper we present several partitioned procedures for time-integrating this coupled problem and discuss their merits in terms of accuracy, stability, heterogeneous computing, I/O transfers, subcycling and parallel processing. All theoretical results are derived for a one-dimensional piston model problem with a compressible flow, because the complete three-dimensional aeroelastic problem is difficult to analyze mathematically. However, the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of two-dimensional transient aeroelastic response of a flexible panel in a transonic nonlinear Euler flow regime.

### MSC:

 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 74S30 Other numerical methods in solid mechanics (MSC2010) 76H05 Transonic flows 76M25 Other numerical methods (fluid mechanics) (MSC2010)

### Keywords:

piston problem; flexible panel; transonic flow
Full Text:

### References:

 [1] Donea, J., An arbitrary Lagrangian-Eulerian finite element method for transient fluid-structure interactions, Comput. methods appl. mech. engrg., 33, 689-723, (1982) · Zbl 0508.73063 [2] Hughes, T.J.R.; Liu, W.K.; Zimmermann, T.K., Lagrangian-Eulerian finite element: formulation for incompressible viscous flows, () · Zbl 0482.76039 [3] Belytschko, T.; Kennedy, J.M., Computer models for subassembly simulation, Nucl. engrg. des., 49, 17-38, (1978) [4] Kandil, O.A.; Chuang, H.A., Unsteady vortex-dominated flows around maneuvering wings over a wide range of Mach numbers, () [5] Farhat, C.; Lin, T.Y., Transient aeroelastic computations using multiple moving frames of reference, () · Zbl 0819.73072 [6] Batina, J.T., Unsteady Euler airfoil solutions using unstructured dynamic meshes, () [7] Lesoinne, M.; Farhat, C., Stability analysis of dynamic meshes for transient aeroelastic computations, () · Zbl 0991.74069 [8] Park, K.C.; Felippa, C.A., Partitioned analysis of coupled systems, (), 157-219 · Zbl 0546.73063 [9] Borland, C.J.; Rizzetta, D.P., Nonlinear transonic flutter analysis, Aiaa j., 1606-1615, (1982) · Zbl 0495.73044 [10] Shankar, V.; Ide, H., Aeroelastic computations of flexible configurations, Comput. struct., 30, 15-28, (1988) · Zbl 0668.73058 [11] Rausch, R.D.; Batina, J.T.; Yang, T.Y., Euler flutter analysis of airfoils using unstructured dynamics meshes, () [12] Blair, M.; Williams, M.H.; Weisshaar, T.A., Time domain simulations of a flexible wing in subsonic compressible flow, () [13] Strganac, T.W.; Mook, D.T., Numerical model of unsteady subsonic aeroelastic behavior, Aiaa j., 28, 903-909, (1990) [14] Pramono, E.; Weeratunga, S.K., Aeroelastic computations for wings through direct coupling on distributed-memory MIMD parallel computers, () [15] Hughes, T.J.R.; Liu, W.K., Implicit-explicit finite elements in transient analysis: stability theory, ASME J. appl. mech., 45, 371-374, (1978) · Zbl 0392.73076 [16] Belytschko, T.; Smolenski, P.; Liu, W.K., Stability of multi-time step partitioned integrators for first-order finite element systems, Comput. methods appl. mech. engrg., 49, 281-297, (1985) · Zbl 0599.65060 [17] Fung, Y.C., An introduction to the theory of aeroelasticity, (), 160-185 [18] Schlichting, H., Boundary layer theory, (1960), McGraw-Hill New York · Zbl 0096.20105 [19] Hughes, T.J.R., (), 67-155 [20] Farhat, C.; Park, K.C.; Pelerin, Y.D., An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems, Comput. methods appl. mech. engrg., 85, 349-365, (1991) · Zbl 0764.73081 [21] Farhat, C.; Sobh, N., A consistency analysis of a class of concurrent transient implicit/explicit algorithms, Comput. methods appl. mech. engrg., 84, 147-162, (1990) · Zbl 0726.73069 [22] C. Farhat, M. Lesoinne and N. Maman, Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution, Int. J. Numer. Methods Fluids, in press. · Zbl 0865.76038 [23] Maman, N.; Farhat, C.; Maman, N.; Farhat, C., Matching fluid and structure meshes for aeroelastic computations: a parallel approach, (), Comput. struct., 54, 4, 779-785, (1993) [24] Crivelli, L.; Farhat, C., Implicit transient finite element structural computations on MIMD systems: FETI vs. direct solvers, () [25] Farhat, C.; Crivelli, L.; Roux, F.X., Extending substructure based iterative solvers to multiple load and repeated analyses, Comput. methods appl. mech. engrg., 117, 195-210, (1994) · Zbl 0851.73059 [26] Farhat, C.; Fezoui, L.; Lanteri, S., Two-dimensional viscous flow computations on the connection machine: unstructured meshes, upwind schemes, and massively parallel computations, Comput. methods appl. mech. engrg., 102, 61-88, (1991) · Zbl 0767.76049 [27] Barszcz, E., Intercube communication on the ipsc/860, () [28] Piperno, S., Numerical methods used in aeroelasticity simulations, Rapport CERMICS 92-5, (October, 1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.