Updated Lagrangian free surface flow simulations with natural neighbour Galerkin methods

International Journal for Numerical Methods in Engineering

Volumn 60, Issue 13, 2004, Pages 2105-2129

  Martinez M A ^a   Cueto, E ^a   Alfaro, I ^a   Doblare M ^a   Chinesta, F ^b  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b CNRS   (France)

Author keywords

Meshless methods; Natural element method; Newtonian fluid; Norton Hoff plasticity; Short fibre reinforced thermoplastics; X shapes

Indexed keywords

COMPUTER SIMULATION; FLOW OF FLUIDS; GALERKIN METHODS; NEWTONIAN LIQUIDS; VISCOPLASTICITY;

NATURAL ELEMENT METHOD (NEM); SURFACE FLOW;

LAGRANGE MULTIPLIERS;

FLUID FLOW; FREE SURFACE FLOW; LAGRANGIAN ANALYSIS; MATHEMATICAL METHOD; NEWTONIAN FLUID; VISCOPLASTICITY;

EID: 3843072290     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1036     Document Type: Article

References (33)

1. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
2. Babuška I, Melenk JM. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:727-758.
3. Liu WK, Jun S, Li S, Adee J, Belytschko T. Reproducing kernel particle methods. International Journal for Numerical Methods in Engineering 1995; 38:1655-1679.
4. Duarte CAM, Oden JT. An H-p adaptive method using clouds. Computer Methods in Applied Mechanics and Engineering 1996; 139:237-262.
5. Atluri SN, Zhu T. New concepts in meshless methods. International Journal for Numerical Methods in Engineering 2000; 47:537-556.
6. De S, Bathe KJ. Towards an efficient meshless computational technique: the method of finite spheres. Engineering Computations 2001; 18:170-192.
7. Lewis RW, Navti SE, Taylor C. A mixed lagrangian-eulerian approach to modelling fluid flow during mould filling. International Journal for Numerical Methods in Engineering 1997; 25:931-952.
8. Donea J. Arbitrary Lagrangian-Eulerian finite element methods. In Computer Methods for Transient Analyses Belytschko T, Hughes TJR (eds). Elsevier: Amsterdam, 1983; 474-516.
9. Montón I, Torres R, Chinesta F, Poitou A. A 3d mold filling simulation for short fibres reinforced thermoplastics. European Congress on Computational Methods in Applied Sciences and Engineering, 2000.
10. Sussman M, Smereka P, Osher S. A level set approach for computing solutions to incompressible two-phase flows. Journal of Computational Physics 1994; 114:146-149.
11. Sukumar N, Moran B, Belytschko T. The natural element method in solid mechanics. International Journal for Numerical Methods in Engineering 1998; 43(5):839-887.
12. Cueto E, Doblaré M, Gracia L. Imposing essential boundary conditions in the natural element method by means of density-scaled α-shapes. International Journal for Numerical Methods in Engineering 2000; 49-4:519-546.
13. Cueto E, Calvo B, Doblaré M. Modeling three-dimensional piece-wise homogeneous domains using the α-shape based natural element method. International Journal for Numerical Methods in Engineering 2002; 54:871-897.
14. Edelsbrunner H, Kirkpatrick DG, Seidel R. On the shape of a set of points in the plane. IEEE Transactions on Information Theory, 1983; IT-29(4):551-559.
15. Edelsbrunner H. Mücke E. Three dimensional alpha shapes. ACM Transactions on Graphics 1994; 13:43-72.
16. Sibson R. A brief description of natural neighbour interpolation. In Interpreting Multivariate Data, Barnett V (ed.). Wiley: New York, 1981; 21-36.
17. Belikov VV, Yu Semenov A. Non-Sibsonian interpolation on arbitrary system of points in Euclidean space and adaptive isolines generation. Applied Numerical Mathematics 2000; 32(4):371-387.
18. Hiyoshi H, Sugihara K. Two generalizations of an interpolant based on Voronoi diagrams. International Journal of Shape Modeling 1999; 5(2):219-231.
19. Cueto E, Sukumar N, Calvo B, Cegonino J, Doblaré M. Overview and recent advances in natural neighbour Galerkin methods. Archives of Computational Methods in Engineering 2003; 10(4):307-384.
20. Sibson R. A vector identity for the Dirichlet tesselation. Mathematical Proceedings of the Cambridge Philosophical Society 1980; 87:151-155.
21. Sukumar N, Moran B, Yu Semenov A, Belikov VV. Natural neighbor Galerkin methods. International Journal for Numerical Methods in Engineering 2001; 50(1):1-27.
22. 1 natural neighbour interpolant for partial differential equations. Numerical Methods for Partial Differential Equations 1999: 15(4):417-447.
23. Cueto E. Cegonino J, Calvo B, Doblaré M. On the imposition of essential boundary conditions in natural neighbour Galerkin methods. Communications in Numerical Methods in Engineering 2003; 19(5):361-376.
24. 1 surface interpolation. In Mathematical Software III, Rice JR (ed.), vol. 3. Academic Press: New York, 1977.
25. Chinesta F, Poitou A, Torres R. Numerical simulation of the steady recirculating flows of fiber suspensions. Journal of Non-Newtonian Fluid Mechanics 2000; 90:65-80.
26. Azaiez J, Chiba K, Chinesta F, Poitou A. State-of-the-art on numerical simulation of fiber-reinforced thermoplastic forming processes. Archives of Computational Methods in Engineering 2002; 9-2:141-198.
27. Sukumar N. The natural element method in solid mechanics. Ph.D. Thesis, Northwestern University, Evanston, Illinois, 1998.
28. Martinez MA, Cueto E, Doblaré M, Chinesta F. Natural element meshless simulation of injection processes involving short fiber suspensions. Journal of Non-Newtonian Fluid Mechanics 2003; 115:51-78.
29. Farin G. Surfaces over Dirichlet tesselations. Computer Aided Geometric Design 1990; 7(1-4):281-292.
30. Preparata F, Shamos M. Computational Geometry: An Introduction. Springer: New York, 1985.
31. Teichmann M, Capps M. Surface reconstruction with anisotropic density-scaled alpha shapes. In Proceedings of the 1998 IEEE Visualization Conference. North Carolina, USA, 1998.
32. Pichelin E, Coupez T. Finite element solution of the 3D mold filling problem for viscous incompressible fluid. Computer Methods in Applied Mechanics and Engineering 1998; 163:359-371.
33. Bonet J, Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. International Journal for Numerical Methods in Engineering 2000; 47:1189-1214.