Deriving Adequate Formulations for Fluid-Structure Interaction Problems: from ALE to Transpiration
Keywords:
fluid-structure interaction, large deformation, time discretisation, otal energy conservation, linearisation, transpirationAbstract
Most formulations describing low speed large displacements fluid-structure interaction problems use a totally lagrangian formulation for the structure, and an Arbitrary Euler Lagrange (ALE) formulation for the fluid. The purpose of the presellt paper is to review the derivation of such formulations, to describe different time discretisation strategies and to explain the type of numerical problems which arise when implementing these techniques. To overcome all technical difficulties arising when dealing with moving grids, we will also explain how an adequate asymptotic expansion can reduce the problem to a standard problem written on a fixed configuration, but using specific transpiration illterface boundary conditions. This last formulation is rather popular in the aeronautical community, and will be illustrated by various numerical experiments.
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References
[AGA 82] AGARD, Ed., Compendium of Unsteady Aerodynamic Measurements, num. 702,
Advisory Group for Aerospace Research and Development, North Atlantic Treaty Organization,
[BAS 99] BASTIN J., ROGE G., "A Multidimensional Fluctuation Splitting Scheme for the
Three-Dimensional Euler Equations", M2AN Math. Model. Numer. Anal., vol. 33, num. 6,
, pp. 1241-1259.
[CAR 95] CARRIVE-BEDOUANI M., LE TALLEC P., MOURO J., "Approximations par elements
finis d'un modele de coques minces geometriquement exact", Rev. Europeenne Elbn.
Finis, vol. 4, num. 5-6, 1995, pp. 633-661.
[DAU 84] DAUTRAY R., LIONS J. L., Analyse mathematique et calcul numerique pour les
sciences et les techniques, Collection du Commissariat a I'Energie Atomique, Masson,
[FAR 98a] FARHAT C., LESOINNE M., LE TALLEC 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. MethodsAppl. Mech. Engrg., vol. 157, num. 1-2,1998, pp. 95-114.
[FAR 98b] FARHAT C., LESSOINNE M., "Higher-order Ataggered and Subiteration Free Algorithm
for Coupled Dynamic Aeroelasticity Problems", AIAA Paper 98-0516, 36th
Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 1998.
[FAU 98] FAURE C., PAPEGAY Y., "08yssee User's Guide Version 1.7", report
num. RT0224, 1998, INRIA.
[FEZ 89] FEZOUI L., STOUFFLET B., "A Class of Implicit Upwind Schemes for Euler Simulations
with Unstructured Meshes", J. Comput. Phys., vol. 84, num. I, 1989, pp. 174-206.
[KOO 98] KOOBUS B., FARHAT C., "Second Order Implicit Schemes that Satisfy the GCL for
Flow Computations on Dynamic Grids'", A1AA Paper 98-0113, 36th Aerospace Sciences
Meeting and Exhibit, Reno, Nevada, January 1998.
[KUH 99] KUHL D., RAMM E., "Generalized Energy-Momentum Method for Non-Linear
Adaptive Shell Dynamics". Comput. Methods Appl. Mech. Engrg .. vol. 178, num. 3-4,
, pp. 343-366.
[LET 94] LE TALLEC P., Numerical Methods for Non-Linear Three-Dimensional Elasticity.
vol. III of Handbook of Numerical Analysis, North Holland, 1994.
[LET 96] LE TALLEC P., MOURO J., "Structures en grands deplacements couplees a des ftuides
en mouvement'", report num. RR2961, August 1996, INRIA.
[LET 99a] LE TALLEC P .. MAN! S., "Analysis of a Linearised Fluid Structure Interaction
Problem", report num. 9917. May 1999, CEREMADE Universite de Paris Dauphine, to
appear in Numerische Mathematik.
[LET 99b] LE TALLEC P., MOURO J., "Fluid Structure Interaction with Large Structural Displacements'".
, to appear in Computer Methods in Applied Mechanics and Engineering.
[LIG 58] LIGHTHILL M. 1., "On Displacement Thickness", J. Comput. Phys., vol. 4, 1958,
pp. 383-392.
[MAR 96) MARTIN R., GUILLARD H., "Second-Order Defect-Correction Scheme for Unsteady
Problems", Computer Fluids, vol. 25, num. I, 1996, pp. 9-27.
[PIP 95a] PIPERNO S., "Simulation numerique de phenomenes d'interaction fluide structure",
PhD thesis, Ecole Nationale des Ponts et Chaussees, 1995.
[PIP 95b) PIPERNO S., FARHAT C., LARROUTUROU B., "Partitioned Procedures for the Transient
Solution of Coupled Aeroelastic Problems", Comput. Methods Appl. Mech. Engrg.,
vol. 124, 1995, pp. 79-111.
[SEL 89) SELMIN V., "A Multistage Method for the Solution of the Euler Equations on Unstructured
Grids", GRUBER R., PERIAUX 1., SHAW R. P., Eds., Proceedings of the 5th
International Symposium on Numerical Methods in Engineering, vol. 2, Springer-Verlag,
, pp. 449-454.
[SIM 92) SIMO 1. C., TARNOW N., "The Discrete Energy-Momentum method. Conserving
Algorithms for Non-Linear Elastodynamics", Z. Angew. Math. Phys., vol. 43, num. 5,
, pp. 757-792.
