A monolithic approach to fluid-structure interaction. (English) Zbl 1053.76042
Summary: This paper compares partitioned and monolithic solution procedures for numerical simulation of fluid-structure interactions. Their different stability properties are illustrated, and the role of structural prediction for a partitioned method is discussed. A grid refinement study is carried out to assess the temporal accuracy of these methods. Moreover, their computational cost as well as their computational efficiency are compared. Numerical experiments are presented for a one-dimensional model problem of a piston interacting with fluid.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76N15 | Gas dynamics (general theory) |
| 76F10 | Shear flows and turbulence |
References:
| [1] | Felippa, C. A.; Park, K. C.; Farhat, C., Partitioned analysis of coupled mechanical systems, Comput. Methods Appl. Mech. Engrg., 190, 3247-3270 (2001) · Zbl 0985.76075 |
| [2] | Piperno, S.; Farhat, C.; Larrouturou, B., Partitioned procedures for the transient solution of coupled aeroelastic problems-Part I: Model problem, theory and two-dimensional applications, Comput. Methods Appl. Mech. Engrg., 124, 79-112 (1995) · Zbl 1067.74521 |
| [3] | Piperno, S.; Farhat, C., Partitioned procedures for the transient solution of coupled aeroelastic problems-Part II: energy transfer analysis and three-dimensional applications, Comput. Methods Appl. Mech. Engrg., 190, 3147-3170 (2001) · Zbl 1015.74009 |
| [4] | Piperno, S., Explicit/implicit fluid/structure staggered procedures with a structural predictor and fluid subcycling for 2d inviscid aeroelastic simulations, Int. J. Numer. Methods Fluids, 25, 1207-1226 (1997) · Zbl 0910.76065 |
| [5] | LeTallec, P.; Mouro, J., Fluid-structure interaction with large structural displacements, Comput. Methods Appl. Mech. Engrg., 190, 3039-3067 (2001) · Zbl 1001.74040 |
| [6] | Blom, F. J., A monolithical fluid-structure interaction algorithm applied to the piston problem, Comput. Methods Appl. Mech. Engrg., 167, 369-391 (1998) · Zbl 0948.76046 |
| [7] | Alonso, J. J.; Jameson, A., Fully-implicit time-marching aeroelastic solutions, AIAA, 0056, 1-13 (1994) |
| [8] | Morton, S. A.; Melville, R. B.; Visbal, M. R., Accuracy and coupling issues of aeroelastic Navier-Stokes solutions on deforming meshes, AIAA, 1085, 252-262 (1997) |
| [9] | Shakib, F.; Hughes, T. J.R.; Johan, Z., A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 89, 141-219 (1991) · Zbl 0838.76040 |
| [10] | Hauke, G.; Hughes, T. J.R., A comparative study of different sets of variables for solving compressible and incompressible flows, Comput. Methods Appl. Mech. Engrg., 153, 1-44 (1998) · Zbl 0957.76028 |
| [11] | Hughes, T. J.R., The finite element method-Linear static and dynamic finite element analysis (2000), Dover Publishers: Dover Publishers New York · Zbl 1191.74002 |
| [12] | van Brummelen EH, Hulshoff SJ, de Borst R. Energy conservation under incompatibility for fluid-structure interaction problems. In: Mang HA, Rammerstorfer FG, Eberhardsteiner J, editors. Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V) Vienna University of Technology, July 7-12, 2002. Available from: http://wccm.tuwien.ac.at/publications/Papers/fp81596.pdf; van Brummelen EH, Hulshoff SJ, de Borst R. Energy conservation under incompatibility for fluid-structure interaction problems. In: Mang HA, Rammerstorfer FG, Eberhardsteiner J, editors. Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V) Vienna University of Technology, July 7-12, 2002. Available from: http://wccm.tuwien.ac.at/publications/Papers/fp81596.pdf |
| [13] | van Brummelen, E. H.; Hulshoff, S. J.; de Borst, R., Energy conservation under incompatibility for fluid-structure interaction problems, Comput. Methods Appl. Mech. Engrg., 192, 2727-2748 (2003) · Zbl 1054.74567 |
| [14] | Michler, C.; van Brummelen, E. H.; Hulshoff, S. J.; de Borst, R., The relevance of conservation for stability and accuracy of numerical methods for fluid-structure interaction, Comput. Methods Appl. Mech. Engrg., 192, 4195-4215 (2003) · Zbl 1181.74156 |
| [15] | Michler C, Hulshoff S, van Brummelen H, Bijl H, de Borst R. Space-time discretizations for fluid-structure interaction. In: Mang HA, Rammerstorfer FG, Eberhardsteiner J, editors. Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), Vienna University of Technology, July 7-12, 2002. Available from: http://wccm.tuwien.ac.at/publications/Papers/fp80130.pdf; Michler C, Hulshoff S, van Brummelen H, Bijl H, de Borst R. Space-time discretizations for fluid-structure interaction. In: Mang HA, Rammerstorfer FG, Eberhardsteiner J, editors. Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), Vienna University of Technology, July 7-12, 2002. Available from: http://wccm.tuwien.ac.at/publications/Papers/fp80130.pdf |
| [16] | Piperno S. Simulation numérique de phénomènes d’interaction fluide-structure. PhD thesis, Ecole Nationale des Ponts et Chaussées, France, 1995 (partly in French); Piperno S. Simulation numérique de phénomènes d’interaction fluide-structure. PhD thesis, Ecole Nationale des Ponts et Chaussées, France, 1995 (partly in French) |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
