On spurious velocities in incompressible flow problems with interfaces

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 7, 2007, Pages 1193-1202

  Ganesan, Sashikumaar ^a   Matthies, Gunar ^b   Tobiska, Lutz ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Finite elements; Incompressible flow; Interface; Two phase flow

Indexed keywords

CALCULATIONS; FINITE ELEMENT METHOD; TWO PHASE FLOW; VELOCITY;

INCOMPRESSIBILITY CONSTRAINT; LOCAL EXTERNAL FORCE; NON-PHYSICAL VELOCITY;

INCOMPRESSIBLE FLOW;

CALCULATIONS; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; TWO PHASE FLOW; VELOCITY;

EID: 33750953440     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.08.018     Document Type: Article

References (18)

1. P. Gresho, R. Lee, S. Chan, J. Leone, A new finite element for incompressible or Boussinesq fluids, in: Proc. Third Int. Conf. on Finite Elements in Flow Problems, Banff, Canada, 1980, pp. 204-215.
2. Pelletier D., Fortin A., and Camarero R. Are FEM solutions of incompressible flows really incompressible? (Or how simple flows can cause headaches!). Int. J. Numer. Methods Fluids 9 (1989) 99-112
3. O. Dorok, Eine stabilisierte Finite-Elemente-Methode zur Lösung der Boussinesq-Approximation der Navier-Stokes-Gleichungen, Ph.D. thesis, Otto-von-Guericke-Universität (1995).
4. Gerbeau J.-F., le Bris C., and Bercovier M. Spurious velocities in the steady flow of an incompressible fluid subjected to external forces. Int. J. Numer. Methods Fluids 25 (1997) 679-695
5. Lafaurie B., Nardone C., Scardovelli R., Zaleski S., and Zanetti G. Modelling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys. 113 (1994) 134-147
6. Fortin M., and Fortin A. Experiments with several elements for viscous incompressible flows. Int. J. Numer. Methods Fluids 5 (1985) 911-928
7. O. Dorok, W. Grambow, L. Tobiska, Aspects of finite element discretizations for solving the Boussinesq approximation of the Navier-Stokes equations., in: F.-K. Hebeker, R. Rannacher, G. Wittum (Eds.), Numerical Methods for the Navier-Stokes Equations. Notes on Numerical Fluid Mechanics, vol. 47. Proceedings of the International Workshop held at Heidelberg, October 25-28, 1993, Vieweg, Braunschweig, 1994, pp. 50-61.
8. Ganesan S., and John V. Pressure separation - a technique for improving the velocity error in finite element discretisations of the Navier-Stokes equations. Appl. Math. Comp. 165 (2005) 275-290
9. Girault V., and Raviart P.-A. Finite Element Methods for Navier-Stokes equations (1986), Springer-Verlag, Berlin, Heidelberg, New York
10. disc element in arbitrary space dimensions. Computing 69 2 (2002) 119-139
11. Ruschak K. A method for incorporating free boundaries with surface tension in finite element fluid-flow simulators. Int. J. Numer. Meth. Engng. 15 (1980) 639-648
12. Dziuk G. Finite elements for the Beltrami operator on arbitrary surfaces. In: Hildebrandt S., and Leis R. (Eds). Partial Differential Equations and Calculus of Variations (1988), Springer, Berlin 142-155
13. Dziuk G. An algorithm for evolutionary surfaces. Numer. Math. 58 6 (1991) 603-611
14. E. Bänsch, Numerical methods for the instationary Navier-Stokes equations with a free capillary surface, Habilitationsschrift, Albert-Ludwigs-Universität, Freiburg i. Br., 1998.
15. Bänsch E. Finite element discretization of the Navier-Stokes equations with a free capillary surface. Numer. Math. 88 2 (2001) 203-235
16. Gilbarg D., and Trudinger N.S. Elliptic partial differential equations of second order (2001), Springer-Verlag, Berlin reprint of the 1998 edition
17. John V., Knobloch P., Matthies G., and Tobiska L. Non-nested multi-level solvers for finite element discretisations of mixed problems. Computing 68 4 (2002) 313-341
18. John V., and Matthies G. MooNMD - a program package based on mapped finite element methods. Comput. Vis. Sci. 6 2-3 (2004) 163-170