Abstract
This paper presents a novel mesh-update technique for unsteady free-surface Newtonian flows using spectral element method and relying on the arbitrary Lagrangian–Eulerian kinematic description for moving the grid. Selected results showing compatibility of this mesh-update technique with spectral element method are given
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Deville M.O., Fischer P.F., and Mund E.H. (2002). High-Order Methods for Incompressible Fluid Flow. Cambridge University Press, Cambridge ISBN 0-521-45309-7
Donea J. (1983). Arbitrary Lagrangian–Eulerian finite element methods. In: Belytschko T.B., and Hugues T.J.R (eds). Computational Methods for Transient Analysis, North Holland pp. 474–516
Farhat C., Geuzaine P., and Grandmont C. (2001). The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids. J. Comput. Phys 174:669–694
Farhat C., and Geuzaine P. (2004). Design and analysis of robust ALE time-integrators for the solution of unsteady flow problems on moving grids. Comput. Meth. Appl. Mech. Engng 193:4073–4075
Formaggia L., and Nobile F. (2004). Stability analysis of second-order time accurate schemes for ALE–FEM. Comput. Meth. Appl. Mech. Engng 193:4097–4116
Güler I., Behr M., and Tezduyar T.E. (1999). Parallel finite element computation of free-surface flows. Comput. Mech 23:117–123
Hirt C.W., Amsden A.A., and Cook J.L. (1974). An arbitrary Lagrangian–Eulerian computing method for all flow speeds. J. Comput. Phys 14:227–253
Ho L.W., and Patera A.T. (1990). A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows. Comput. Meth. Appl. Mech. Engng 80:355–366
Hodges B.R., and Street R.L. (1999). On simulation of turbulent nonlinear free-surface flows. J. Comput. Phys 151:425–457
Johnson A.A., and Tezduyar T.E. (1994). Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput. Meth. Appl. Mech. Engng 119:73–94
Karniadakis G.E., Israeli M., and Orszag S.A. (1991). High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys 97:414–443
Lee N.S., and Bathe K.J. (1994). Error indicators and adaptive remeshing in large deformation finite element analysis. Finite Elements Anal. Design 16:99–139
Maday Y., and Patera A.T. (1989). 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. ASME, New-York, pp. 71–142
Patera A.T. (1984). Spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys 54: 468–488
Ramaswamy B., and Kawahara M. (1987). Arbitrary Lagrangian–Eulerian finite-element method for unsteady, convective, incompressible viscous free-surface fluid-flow. Int. J. Numer. Meth. Fl 7(10):1053–1075
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Bouffanais, R., Deville, M.O. Mesh Update Techniques for Free-Surface Flow Solvers Using Spectral Element Method. J Sci Comput 27, 137–149 (2006). https://doi.org/10.1007/s10915-005-9050-z
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DOI: https://doi.org/10.1007/s10915-005-9050-z