Solution of moving-boundary problems by the spectral element method

Applied Numerical Mathematics

Volumn 58, Issue 7, 2008, Pages 968-984

  Bodard, Nicolas ^a   Bouffanais, Roland ^a   Deville, Michel O ^a  

^a EPFL   (Switzerland)

Author keywords

Moving boundary problem; Moving grid; Spectral element method

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; SPECTRUM ANALYSIS;

MOVING BOUNDARY PROBLEMS; SPECTRAL ELEMENT METHOD;

PROBLEM SOLVING;

EID: 43849106934     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2007.04.009     Document Type: Article

References (25)

1. Bodard N., and Deville M.O. Fluid-structure interaction by the spectral element method. J. Sci. Comput. 27 (2006) 123-136
2. Bouffanais R., and Deville M.O. Mesh update techniques for free-surface flow solvers using spectral element method. J. Sci. Comput. 27 (2006) 137-149
3. Deville M.O., Fischer P.F., and Mund E.H. High-Order Methods for Incompressible Fluid Flow (2002), Cambridge University Press, Cambridge
4. Donea J. Arbitrary Lagrangian-Eulerian finite element methods. In: Belytschko T.B., and Hugues T.J.R. (Eds). Computational Methods for Transient Analysis (1983), North-Holland, Amsterdam 474-516
5. Donea J., Huerta A., Ponthot J.-P., and Rodriguez-Ferran A. Arbitrary Lagrangian-Eulerian methods. Fundamentals. In: Stein E., de Borst R., and Hugues T.J.R. (Eds). Encyclopedia of Computational Mechanics vol. 1 (2004), Wiley, New York (Chapter 14)
6. Formaggia L., and Nobile F. A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements. East-West J. Numer. Math. 7 (1999) 105-132
7. Gordon W.J., and Hall C.A. Construction of curvilinear coordinate systems and application to mesh generation. Int. J. Numer. Methods Eng. 7 (1973) 461-477
8. Hirt C.W., Amsden A.A., and Cook J.L. An Arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14 (1974) 227-253
9. Ho L.-W., and Patera A.T. A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows. Comput. Methods Appl. Mech. Engrg. 80 (1990) 355-366
10. Ho L.-W., and Patera A.T. Variational formulation of three-dimensional viscous free-surface flows: Natural imposition of surface tension boundary conditions. Int. J. Numer. Methods Fluids 13 (1991) 691-698
11. Karniadakis G.E., Israeli M., and Orszag S.A. High-order splitting methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 97 (1991) 414-443
12. Lamb H. Hydrodynamics. sixth ed. (1932), Cambridge University Press
13. Maday Y., and Patera A.T. Spectral element methods for the incompressible Navier-Stokes equations. In: Noor A.K., and Oden J.T. (Eds). State-of-the-Art Survey on Computational Mechanics (1989), ASME, New York 71-142
14. N - 2 method for the approximation of the Stokes problem, Tech. Rep. 92009, Department of Mechanical Engineering, MIT, Cambridge, MA, 1992
15. F. Nobile, Numerical approximation of fluid-structure interaction problems with application to haemodynamics, Ph.D. thesis, no. 2458, Swiss Federal Institute of Technology, Lausanne, 2001
16. Patera A.T. Spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 65 (1986) 474-480
17. Perot J.B. An analysis of the fractional step method. J. Comput. Phys. 108 (1993) 51-58
18. Perot J.B. Comments on the fractional step method. J. Comput. Phys. 121 (1995) 190-191
19. Quarteroni A., and Valli A. Numerical Approximation of Partial Differential Equations. Springer Series in Computational Mathematics (1994), Springer, Berlin
20. Rønquist E.M. A domain decomposition solver for three-dimensional steady free surface flows. In: Bjørstad P., Espedal M., and Keyes D. (Eds). Domain Decomposition 9 Proceedings (1998), Wiley, New York 792-801
21. E.M. Rønquist, Spectral element methods for the unsteady Navier-Stokes equations, von Kármán Institute for Fluid Dynamics, Lecture Series 1991-01 (February 18-22, 1991)
22. Scardovelli R., and Zaleski S. Direct numerical simulation of free-surface and interfacial flow. Annu. Rev. Fluid Mech. 31 (1999) 567-603
23. C.R. Schneidesch, Numerical simulation of incompressible flows in complex geometries by preconditioned Chebyshev collocation, Ph.D. thesis, Université Catholique de Louvain, Louvain-La-Neuve, 1992
24. Schneidesch C.R., and Deville M.O. Chebyshev collocation method and multi-domain decomposition for Navier-Stokes equations in complex curved geometries. J. Comp. Phys. 106 (1993) 234-257
25. Tsai W.-T., and Yue D.K.P. Computation of nonlinear free-surface flows. Annu. Rev. Fluid Mech. 28 (1996) 249-278