Fixed-grid methods for moving interface problems offer a number of attractive properties and have therefore gained quite some popularity in recent time. In [9], we introduced a fixed-grid method based on eXtended Finite Element Method (XFEM) and Lagrange Multiplier (LM) techniques. This paper reviews the original method and its enhancements towards realistic problems. Major challenges are the proper resolution of flow features near the fluid-structure interface for which two enhancements are discussed: a straightforward approach based on local adaptivity and a hybrid method that combines ideas from fixed-grid methods and Arbitrary Lagrangean Eulerian formulations. Necessary steps, which we introduce in [11], to enhance the XFEM/LM-FSI-method for three-dimensional higher-order problems are explained.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
I. M. Babuška, J. M. Melenk, The partition of unity method, International Journal for Numerical Methods in Engineering 40 (4) (1997) 727–758
M. Behr, T. E. Tezduyar, The shear-slip mesh update method, Computer Methods in Applied Mechanics and Engineering 174 (1999) 261–274
T. Belytschko, T. Black, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering 45 (5) (1999) 601–620
C. Bernardi, Y. Maday, A. T. Patera, Asymptotic and numerical methods for partial differen tial equations with critical parameters, vol. 384, chap. Domain decomposition by the mortar element method, Reidel, Dordrecht, 1993, pp. 269–286
C. Bernardi, Y. Maday, A. T. Patera, A new nonconforming approach to domain decomposi tion: the mortar element method, Nonlinear partial differential equations and their applications 299 (1994) 13–51
C. Förster, W. A. Wall, E. Ramm, On the geometric conservation law in transient flow calcu lations on deforming domains, International Journal for Numerical Methods in Fluids 50 (12) (2006) 1369–1379
C. Förster, W. A. Wall, E. Ramm, Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows, Computer Methods in Applied Mechanics and Engineering 196 (7) (2007) 1278–1293
A. Gerstenberger, W. A. Wall, Efficient treatment of moving interfaces on fixed grids for sur face coupled problems, International Journal for Numerical Methods in Fluids, accepted, DOI: 10.1002/fld.1782
A. Gerstenberger, W. A. Wall, An extended finite element method/Lagrange multiplier based approach for fluid-structure interaction, Computer Methods in Applied Mechanics and Engineering 197 (19–20) (2008) 1699–1714
U. Küttler, W. A. Wall, Fixed-point fluid-structure interaction solvers with dynamic relaxation, Computational Mechanics 43 (2008) 61–72
U. M. Mayer, A. Gerstenberger, W. A. Wall, Interface handling for three-dimensional higher-order xfem computations in fluid-structure interaction, International Journal for Numerical Methods in Engineering, submitted
R. L. Meakin, N. E. Suhs, Unsteady aerodynamic simulation of multiple bodies in relative motion, AIAA Paper 89-1996-CP
N. Moës, J. Dolbow, T. Belytschko, A finite element method for crack growth with out remeshing, International Journal for Numerical Methods in Engineering 46 (1) (1999) 131–150
P. Solin, J. Cerveny, I. Dolezel, Arbitrary-level hanging nodes and automatic adaptivity in the hp-fem, Mathematics and Computers in Simulation, in press, Corrected Proof (2007)
J. L. Steger, F. C. Dougherty, J. A. Benek, A Chimera grid scheme, in: K. N. Ghia, U. Ghia (eds.), Advances in Grid Generation, vol. 5, American Society of Mechanical Engineers, FED, New York, 1983
T. E. Tezduyar, S. Sathe, Modelling of fluid-structure interactions with the space-time finite elements: solution techniques, International Journal for Numerical Methods in Fluids 54 (6–8) (2007) 855–900
W. A. Wall, P. Gamnitzer, A. Gerstenberger, Fluid-structure interaction approaches on fixed grids based on two different domain decomposition ideas, International Journal of Computational Fluid Dynamics, 22 (2008) 411–427
W. A. Wall, A. Gerstenberger, P. Gamnitzer, C. Förster, E. Ramm, Large deformation fluid-structure interaction — Advances in ALE methods and new fixed grid approaches, in: H.-J. Bungartz, M. Schafer (eds.), Fluid-Structure Interaction: Modelling, Simulation, Optimisation, LNCSE, Berlin, Heidelberg, Springer, 2006
Z. J. Wang, V. Parthasarathy, A fully automated Chimera methodology for multiple moving body problems, International Journal for Numerical Methods in Fluids 33 (7) (2000) 919–938
B. I. Wohlmuth, Discretization Methods and Iterative Solvers Based on Domain Decomposition, Berlin, Springer, 2001
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science + Business Media B.V
About this chapter
Cite this chapter
Wall, W.A., Gerstenberger, A., Mayer, U.M. (2009). Advances in Fixed-Grid Fluid Structure Interaction. In: Eberhardsteiner, J., Hellmich, C., Mang, H.A., Périaux, J. (eds) ECCOMAS Multidisciplinary Jubilee Symposium. Computational Methods in Applied Sciences, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9231-2_16
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9231-2_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9230-5
Online ISBN: 978-1-4020-9231-2
eBook Packages: EngineeringEngineering (R0)