Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems.

*(English)*Zbl 0991.74069Summary: Partitioned procedures and staggered algorithms are often adopted for the solution of coupled fluid/structure interaction problems in the time domain. In this paper, we overview two sequential and parallel partitioned procedures that are popular in computational nonlinear aeroelasticity, and address their limitation in terms of accuracy and numerical stability. We propose two alternative serial and parallel staggered algorithms for the solution of coupled transient aeroelastic problems, and demonstrate their superior accuracy and computational efficiency with the flutter analysis of AGARD Wing 445.6. We compare our results with those computed by other investigators, and validate them with experimental data.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74S10 | Finite volume methods applied to problems in solid mechanics |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

##### Keywords:

serial algorithms; parallel algorithms; staggered algorithms; coupled fluid/structure interaction; nonlinear aeroelasticity; flutter; AGARD Wing 445.6
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\textit{C. Farhat} and \textit{M. Lesoinne}, Comput. Methods Appl. Mech. Eng. 182, No. 3--4, 499--515 (2000; Zbl 0991.74069)

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##### 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] | Farhat, C.; Lesoinne, M.; Maman, N., Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution, Int. J. numer. methods fluids, 21, 807-835, (1995) · Zbl 0865.76038 |

[3] | J.T. Batina, Unsteady Euler airfoil solutions using unstructured dynamic meshes, AIAA Paper No. 89-0115, AIAA 27th Aerospace Sciences Meeting, Reno, Nevada, 9-12 January 1989 |

[4] | O.A. Kandil, H.A. Chuang, Unsteady vortex-dominated flows around maneuvering wings over a wide range of Mach numbers, AIAA Paper No. 88-0317, AIAA 26th Aerospace Sciences Meeting, Reno, Nevada, 11-14 January 1988 |

[5] | C. Farhat, T.Y. Lin, Transient aeroelastic computations using multiple moving frames of reference, AIAA Paper No. 90-3053, AIAA Eighth Applied Aerodynamics Conference, Portland, Oregon, 20-22 August 1990 |

[6] | A. Masud, A space-time finite element method for fluid structure interaction, Ph.D. thesis, Stanford University, 1993 |

[7] | M. Lesoinne, C. Farhat, Stability analysis of dynamic meshes for transient aeroelastic computations, AIAA Paper No. 93-3325, 11th AIAA Computational Fluid Dynamics Conference, Orlando, Florida, 6-9 July 1993 |

[8] | C. Farhat, High performance simulation of coupled nonlinear transient aeroelastic problems, AGARD Report R-807, Special Course on Parallel Computing in CFD (l’Aérodynamique numérique et le calcul en parallèle), North Atlantic Treaty Organization (NATO), October 1995 |

[9] | S.A. Morton, R.B. Melville, M.R. Visbal, Accuracy and coupling issues of aeroelastic Navier-Sokes solutions of deforming meshes, AIAA Paper 97-1085, 38th AIAA Structures, Structural Dynamics and Materials Conference, Kissimmee, Florida, 7-10 April 1997 |

[10] | G.P. Guruswamy, Time-accurate unsteady aerodynamic and aeroelastic calculations of wings using Euler equations, AIAA Paper No. 88-2281, AIAA 29th Structures, Structural Dynamics and Materials Conference, Williamsburg, Virginia, 18-20 April 1988 |

[11] | R.D. Rausch, J.T. Batina, T.Y. Yang, Euler flutter analysis of airfoils using unstructured dynamic meshes, AIAA Paper No. 89-13834, 30th Structures, Structural Dynamics and Materials Conference, Mobile, Alabama, 3-5 April 1989 |

[12] | C. Farhat, M. Lesoinne, P.S. Chen, S. Lantéri, Parallel heterogeneous algorithms for the solution of three-dimensional transient coupled aeroelastic problems, AIAA Paper No. 95-1290, AIAA 36th Structural Dynamics Meeting, New Orleans, Louisiana, 10-13 April 1995 |

[13] | Piperno, S.; Farhat, C.; Larrouturou, B., Partitioned procedures for the transient solution of coupled aeroelastic problems, Comput. methods appl. mech. engrg., 124, 79-711, (1995) · Zbl 1067.74521 |

[14] | Strganac, T.W.; Mook, D.T., Numerical model of unsteady subsonic aeroelastic behavior, AIAA journal, 28, 903-909, (1990) |

[15] | E. Pramono, S.K. Weeratunga, Aeroelastic computations for wings through direct coupling on distributed-memory MIMD parallel computers, AIAA Paper No. 94-0095, 32nd Aerospace Sciences Meeting and Exhibit, Reno, 10-13 January 1994 |

[16] | J.M. Smith, Flight loads prediction methods for aircraft, vol. I Euler/Navier-Stokes Aeroelastic Method (ENS3DAE) Technical Development Summary, Version 4.0, WRDC-TR-89-3104, November 1989 |

[17] | S.A. Morton, P.S. Beran, Nonlinear analysis of airfoil flutter at transonic speeds, AIAA Paper No. 95-1905, 13th AIAA Applied Aerodynamics Conference, San Diego, 19-22 June 1995 |

[18] | Gupta, K.K., Development of a finite element aeroelastic analysis capability, J. aircraft, 33, 995-1002, (1996) |

[19] | J. Mouro, Numerical simulation of nonlinear fluid structure interactions problems and application to hydraulic shock-absorbers, in: Proceedings of the Third World Conference on Applications of the Computational Fluid Dynamics, Basel World User Days CFD, 19-23 May 1996 |

[20] | Felippa, C.A.; Geers, T.L., Partitioned analysis of coupled mechanical systems, Engineering computations, 5, 123-133, (1988) |

[21] | S.K. Weeratunga, E. Pramono, Direct coupled aeroelastic analysis through concurrent implicit time integration on a parallel computer, AIAA Paper No. 94-1550, April 1994 |

[22] | Lesoinne, M.; Farhat, C., Geometric conservation laws for flow problems with moving boundaries, and deformable meshes and their impact on aeroelastic computations, Comput. methods appl. mech. engrg., 134, 71-90, (1996) · Zbl 0896.76044 |

[23] | Thomas, P.D.; Lombard, C.K., Geometric conservation law and its application to flow computations on moving grids, AIAA journal, 17, 1030-1037, (1979) · Zbl 0436.76025 |

[24] | Koobus, B.; Farhat, C., Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes, Comput. methods appl. mech. engrg., 170, 103-129, (1999) · Zbl 0943.76055 |

[25] | Roe, P.L., Approximate Riemann solvers, parameter vectors and difference schemes, J. comp. phys., 43, 357-371, (1981) · Zbl 0474.65066 |

[26] | A. Dervieux, Steady Euler simulations using unstructured meshes, Von Kármán Institute Lecture Series, 1985 |

[27] | Van Leer, B., Towards the ultimate conservative difference scheme V: a second-order sequel to Goudonov’s method, J. comput. phys., 32, 361-370, (1979) |

[28] | Farhat, C.; Lantéri, S., Simulation of compressible viscous flows on a variety of MPPs computational algorithms for unstructured dynamic meshes and performance results, Comput. methods appl. mech. engrg., 119, 35-60, (1994) · Zbl 0847.76065 |

[29] | Farhat, C.; Chen, P.S.; Mandel, J., A scalable Lagrange multiplier based domain decomposition method for implicit time-dependent problems, Int. J. numer. methods engrg., 38, 3831-3854, (1995) · Zbl 0844.73077 |

[30] | Harder, R.L.; Desmarais, R.N., Interpolation using surface splines, J. aircraft, 9, 189-191, (1972) |

[31] | M.H.L. Hounjet, B.J.G. Eussen, Outline and application of the NRL aeroelastic simulation method, Nationaal Lucht- En Ruimtevaartlaboratorium, NLR TP 94422 L, 1994 |

[32] | S. Brown, Displacement extrapolations for CFD+CSM aeroelastic analysis, AIAA Paper No. 97-1090, 38th AIAA Structures, Structural Dynamics and Materials Conference, Kissimmee, Florida, 7-10 April 1997 |

[33] | Cebral, J.R.; Lohner, R., Conservative load projection and tracking for fluid-structure problems, AIAA journal, 35, 687-692, (1997) · Zbl 0895.73077 |

[34] | Farhat, C.; Lesoinne, M.; LeTallec, P., Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity, Comput. methods appl. mech. engrg., 157, 95-114, (1998) · Zbl 0951.74015 |

[35] | Maman, N.; Farhat, C., Matching fluid and structure meshes for aeroelastic computations: A parallel approach, Comput. and struc., 54, 779-785, (1995) |

[36] | E.C. Yates, AGARD standard aeroelastic configuration for dynamic response, candidate configuration I. - Wing 445.6, NASA TM-100492, 1987 |

[37] | E.M. Lee-Rausch, J.T. Batina, Wing-flutter boundary prediction using unsteady Euler aerodynamic method, AIAA Paper No. 93-1422, 1993 |

[38] | George, P.L., Improvement on Delaunay based 3D automatic mesh generator, Finite elements in analysis and design, 25, 297-317, (1997) · Zbl 0897.65078 |

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