Computation of free surface flows with a projection FEM in a moving mesh framework

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 41-42, 2003, Pages 4703-4721

  Rabier, Sylvain ^a   Medale, Marc ^a  

^a AIX MARSEILLE UNIVERSITY   (France)

Author keywords

Finite element; Free surface; Gravity and capillary waves; Moving mesh technique; Projection method

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; LIQUID SLOSHING; OSCILLATIONS; SURFACES; VISCOUS FLOW;

SURFACE FLOWS;

COMPUTATIONAL METHODS;

FINITE ELEMENT METHOD;

EID: 0141680818     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(03)00456-0     Document Type: Article

References (35)

1. Shyy W. Udaykumar H.S. Rao M.M. Smith R.W. Computational Fluid Dynamics with Moving Boundaries 1996 Hemisphere Washington, DC
2. Harlow F.H. Welch J.F. Numerical calculation of time-dependant viscous incompressible flow with free surface Phys. Fluids 8 1965 2182
3. Hirt C.W. Nichols B.D. Volume of fluids (VOF) method for the dynamic of free boundaries J. Comput. Phys. 39 1981 201-225
4. Osher S. Sethian J.A. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations J. Comput. Phys. 79 1988 12-49
5. Thompson E. Use of pseudo-concentrations to follow creeping viscous flows during transient analysis Int. J. Numer. Methods Fluids 6 1986 749-761
6. Medale M. Jaeger M. Numerical simulation of incompressible flows with moving interfaces Int. J. Numer. Methods Fluids 24 1997 615-638
7. Hirt C.W. Amsden A.A. Cook J.L. An arbritary Lagrangian-Eulerian computing method for all flow speeds J. Comput. Phys. 14 1974 227-253
8. Belytschko T. Kennedy J.M. Computer models for subassembly simulation Nucl. Engrg. Des. 49 1978 17-38
9. Hughes T.J.R. Liu W.K. Zimmermann T.K. Lagrangian-Eulerian finite element formulation for incompressible viscous flows Comput. Methods Appl. Mech. Engrg. 29 1981 329-349
10. Donea J. Giuliani S. Halleux J.P. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions Comput. Methods Appl. Mech. Engrg. 33 1982 689-723
11. Huerta A. Liu W.K. Viscous flow with large free surface motion Comput. Methods Appl. Mech. Engrg. 69 1988 227-324
12. Souli M. Zolesio J.P. Arbritary Lagrangian-Eulerian and free surface methods in fluids mechanics Comput. Methods Appl. Mech. Engrg. 191 2001 451-466
13. Belytschko T. Liu W.K. Moran B. Nonlinear Finite Elements for Continua and Structures 2000 John Wiley - Sons Ltd.
14. Tezduyar T.E. Behr M. Liou J. A new strategy for finite element computations involving moving boundaries and interfaces-the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests Comput. Methods Appl. Mech. Engrg. 94 1992 339-351
15. Chorin A.J. Numerical solution of the Navier-Stokes equations Math. Comp. 22 1968 745-762
16. Teman R. Une méthode d'approximation de la solution des équations de Navier-Stokes Bull. Soc. Math. France 98 1968 115-152
17. Donea J. Giuliani S. Laval H. Quartapelle L. Finite element solution of the unsteady Navier-Stokes equations by a fractional step method Comput. Methods Appl. Mech. Engrg. 30 1982 53-73
18. Gresho P.M. Chan S.T. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via finite element method that also introduces a nearly consistent mass matrix. Part I and Part II Int. J. Numer. Methods Fluids 11 1990 587-620
19. Gresho P.M. Sani R.L. Incompressible Flow and the Finite Element Method 2000 Wiley New York
20. Guermond J.L. Quartapelle L. Calculation of incompressible viscous flows by an unconditionally stable projection FEM J. Comput. Phys. 132 1997 12-33
21. Guermond J.L. Quartapelle L. On stability and convergence of projection methods based on pressure Poisson equation Int. J. Numer. Methods Fluids 26 1998 1039-1053
22. Guermond J.L. Quartapelle L. On the approximation of the unsteady Navier-Stokes equations by finite element projection methods Numer. Math. 80 1998 207-238
23. Guermond J.L. Quartapelle L. A projection FEM for variable density incompressible flows J. Comput. Phys. 165 2000 167-188
24. Codina R. Vazquez M. Zienkiewicz O. A general algorithm for compressible and incompressible flows. Part III: The semi-implicit form Int. J. Numer. Methods Fluids 27 1998 13-32
25. Sung J. Choi H.G. Yoo J.Y. Time accurate computation of unsteady free surface flows using an ALE-segregated equal-order FEM Comput. Methods Appl. Mech. Engrg. 190 2000 1425-1440
26. Navti S.E. Ravindran K. Taylor C. Lewis R.W. Finite element modelling of surface tension effects using a Lagrangian-Eulerian kinematic description Comput. Methods Appl. Mech. Engrg. 147 1997 41-60
27. Prosperetti A. Motion of two superposed viscous fluids Phys. Fluids 24 7 1981 1217-1223
28. Ramaswany B. Numerical simulation of unsteady viscous free surface flow J. Comput. Phys. 90 1990 396-430
29. Popinet S. Zaleski S. A front-tracking algorithm for accurate representation of surface tension Int. J. Numer. Methods Fluids 30 1999 775-793
30. Ushijima S. Three-dimensional Arbitrary Lagrangian-Eulerian numerical prediction method for non-linear free surface oscillation Int. J. Numer. Methods Fluids 26 1998 605-623
31. Braess H. Wriggers P. Arbitrary Lagrangian Eulerian finite element analysis of free surface flow Comput. Methods Appl. Mech. Engrg. 190 2000 95-109
32. S. Balay, K. Buschelman, W.D. Gropp, D. Kaushik, L. Curfman McInnes, B.F. Smith, 2001, PETSc home page,
33. S. Balay, W.D. Gropp, L. Curfman McInnes, B.F. Smith, PETSc Users Manual, ANL-95/11-Revision 2.1.3, Argonne National Laboratory, 2002
34. Balay S. Gropp W.D. Curfman McInnes L. Smith B.F. Efficient management of parallelism in object oriented numerical software libraries Arge E. Bruaset A.M. Langtangen H.P. Modern Software Tools in Scientific Computing 1997 163-202 Birkhauser Press
35. J.L. Batoz, G. Dhatt, Modlisation des structures par éléments finis, vols. II and III, Hermes, 1991, 1992