An enriched finite element method and level sets for axisymmetric two-phase flow with surface tension

International Journal for Numerical Methods in Engineering

Volumn 58, Issue 13, 2003, Pages 2041-2064

  Chessa, Jack ^a   Belytschko, Ted ^b  

^a UNIVERSITY OF TEXAS AT EL PASO   (United States)

^b Northwestern University   (United States)

Author keywords

Enriched finite element; Level sets; Two phase flow; X FEM

Indexed keywords

CONSTRUCTION; FINITE ELEMENT METHOD; INTERFACES (MATERIALS); SURFACE TENSION;

REMESHING; VELOCITY GRADIENT;

TWO PHASE FLOW;

AXISYMMETRIC FLOW; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; MATHEMATICAL ANALYSIS; SURFACE TENSION; TWO-PHASE FLOW;

EID: 0346152714     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.946     Document Type: Article

References (22)

1. Chessa J, Belytschko T. An extended finite element method for two-phase fluids. Journal of Applied Mechanics (ASME) 2003; 70(1): 10-17.
2. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45(5):601-620.
3. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46:131-150.
4. Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2001; 50(4):993-1013.
5. Sukumar N, Chopp DL, Moës N, Belytschko T. Modeling holes and inclusions by level sets in the extended finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 190(46-47): 6183-6200.
6. Wagner GJ, Moës N, Liu WK, Belytschko T. The extended finite element method for rigid particles in Stokes flow. International Journal for Numerical Methods in Engineering 2001; 51(3):293-313.
7. Chessa J, Smolinski P, Belytschko T. The extended finite element method (XFEM) for solidification problems. International Journal for Numerical Methods in Engineering 2002; 53:1959-1977.
8. Renaud M, Dolbow J. Modeling dendritic solidification with the extended finite element method. In Proceedings of the First MIT Conference on Computational Fluid and Solid Mechanics, Bathe KJ (ed.). Elsevier: Boston. 2001; 1135-1138.
9. Melenk JM, Babuška I. The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 39:289-314.
10. Chessa J, Wang H, Belytschko T. On the construction of blending elements for local partition of unity enriched finite elements. International Journal for Numerical Methods in Engineering 2003; 57(7):1015-1038.
11. Osher S, Sethian JA. Propagation of fronts with curvature based speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 1988; 79:12.
12. Sethian JA. Level Set Methods and Fast Marching Methods. Cambridge University Press: Cambridge, MA. 1999.
13. Babuška I, Melenk JM. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:727-758.
14. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2000.
15. Chorin AJ. Numerical solution of the Navier-Stokes equation. Mathematics of Computation 1968; 23:745-762.
16. Zienkiewicz OC, Codina R. A general algorithm for compressible and incompressible flow, Part I. The split characteristic based scheme. International Journal for Numerical Methods in Fluids 1995; 20:869-885.
17. Zienkiewicz OC, Taylor RL. The Finite Element Method, Volume 3: Fluid Dynamics. Butterworth and Hienemann: Oxford, 2000.
18. Belytschko T, Mullen R. Stability of explicit-implicit mesh partitions in time integration. International Journal for Numerical Methods in Engineering 1978; 12(10):1575-1586.
19. Hughes TJR, Liu WK. Implicit-explicit finite-elements in transient analysis-implementation and numerical examples. Journal of Applied Mechanics (ASME) 1978; 45(2):375-378.
20. Belytschko T, Daniel WJT, Ventura G. A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function. International Journal for Numerical Methods in Engineering 2002; 55(1):101-125.
21. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
22. Clift R, Grace JR, Weber ME. Bubbles, Drops and Particles. Academic Press: New York, 1978.