An ALE based iterative CBS algorithm for non-isothermal non-Newtonian flow with adaptive coupled finite element and meshfree method

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 49-52, 2007, Pages 4911-4933

  Duan, Qinglin ^a   Li, Xikui ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

ALE; CBS; Finite element method; Incompressible non isothermal non Newtonian fluid; Iterative procedure; Meshfree method

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; GALERKIN METHODS; INCOMPRESSIBLE FLOW; INJECTION MOLDING; ITERATIVE METHODS; PLASTIC FLOW; TIME DOMAIN ANALYSIS;

CHARACTERISTIC BASED SPLIT ALGORITHM; FRACTIONAL STEP ALGORITHM; MESHFREE METHOD; POWER LAW;

NON NEWTONIAN FLOW;

COMPUTER SIMULATION; FINITE ELEMENT METHOD; GALERKIN METHODS; INCOMPRESSIBLE FLOW; INJECTION MOLDING; ITERATIVE METHODS; NON NEWTONIAN FLOW; PLASTIC FLOW; TIME DOMAIN ANALYSIS;

EID: 34548719254     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.06.010     Document Type: Article

References (45)

1. Hughes T.J.R., Franca L.P., and Balestra M. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput. Methods Appl. Mech. Engrg. 59 (1986) 85-99
2. Tezduyar T.E., Mittal S., Ray S.E., and Shih R. Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput. Methods Appl. Mech. Engrg. 95 (1992) 221-242
3. Guermond J.L., and Quartapelle L. On stability and convergence of projection methods based on pressure Poisson equation. Int. J. Numer. Methods Fluids 26 (1998) 1039-1053
4. Codina R. Pressure stability in fractional step finite element methods for incompressible flows. J. Comput. Phys. 170 (2001) 112-140
5. Li X., and Duan Q. Meshfree iterative stabilized Taylor-Galerkin and characteristic-based split (CBS) algorithms for incompressible N-S equations. Comput. Methods Appl. Mech. Engrg. 195 (2006) 6125-6145
6. Oñate E. A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation. Comput. Methods Appl. Mech. Engrg. 182 (2000) 355-370
7. Codina R., and Blasco J. Stabilized finite element method for the transient Navier-Stokes equations based on a pressure gradient projection. Comput. Methods Appl. Mech. Engrg. 182 (2000) 277-300
8. Brooks A.N., and Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 32 (1982) 199-259
9. Donea J. A Taylor-Galerkin method for convective transport problems. Int. J. Numer. Methods Engrg. 20 (1984) 101-119
10. Douglas J., and Russel T. Numerical methods for convection dominated problems based on combining the method of characteristics with finite elements or finite difference procedures. SIAM J. Numer. Anal. 19 (1982) 871-885
11. Pironneau O. On the transport-diffusion algorithm and its application to the Navier-Stokes equations. Numer. Math. 38 (1982) 309-332
12. Zienkiewicz O.C., and Codina R. A general algorithm for compressible and incompressible flow - Part I. The split, characteristic based scheme. Int. J. Numer. Methods Fluids 20 (1995) 869-885
13. Lohner R., Morgan K., and Zienkiewicz O.C. The solution of non-linear hyperbolic equations system by the finite element method. Int. J. Numer. Methods Fluids 4 (1984) 1043-1063
14. Codina R. Numerical solution of the incompressible Navier-Stokes equations with Coriolis forces based on the discretization of the total time derivative. J. Comput. Phys. 148 (1999) 467-496
15. Bach P., and Hassager O. An algorithm for the use of the Lagrangian specification in Newtonian fluid mechanics and applications to free-surface flow. J. Fluid Mech. 152 (1985) 173-190
16. Ramaswamy B., and Kawahara M. Lagrangian finite element analysis applied to viscous free surface fluid flow. Imposing essential boundary conditions in mesh-free methods. Int. J. Numer. Methods Fluids 87 (1987) 953-984
17. Hirt C.W., and Nichols B.D. Volume of fluid (VOF) method for the dynamics of free surface boundaries. J. Comput. Phys. 39 (1981) 210-225
18. Thompson E. Use of pseudo-concentrations to follow creeping viscous flows during transient analysis. Int. J. Numer. Methods Fluids 6 (1986) 749-761
19. Osher S., and Sethian J.A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1988) 12-49
20. Noh W.F. A time dependent two space dimensional coupled Eulerian Lagrangian code. Methods Comput. Phys. 3 (1964)
21. Hirt C.W., Amsden A.A., and Cook H.K. An arbitrary Lagrangian-Eulerian method for all flow speeds. J. Comput. Phys. 14 (1974) 227-253
22. Hughes T.J.R., Liu W.K., and Zimmerman T.K. Lagrangian-Eulerian finite element formulation for viscous flows. Comput. Methods Appl. Mech. Engrg. 29 (1981) 329-349
23. Huerta A., and Liu W.K. Viscous flows for large free surface motion. Comput. Methods Appl. Mech. Engrg. 69 (1988) 277-324
24. Belytschko T., Flanagan D.F., and Kennedy J.M. Finite element method with user-controlled meshes for fluid-structure interactions. Comput. Methods Appl. Mech. Engrg. 33 (1982) 689-723
25. Braess H., and Wriggers P. Arbitrary Lagrangian Eulerian finite element analysis of free surface flow. Comput. Methods Appl. Mech. Engrg. 190 (2000) 95-109
26. Huerta A., and Fernández-Méndez S. Imposing essential boundary conditions in mesh-free methods. Comput. Methods Appl. Mech. Engrg. 193 (2004) 1257-1275
27. Belytschko T., Organ D., and Krongauz Y. A coupled finite element-free Galerkin method. Comput. Mech. 17 (1995) 186-195
28. Huerta A., and Fernández-Méndez S. Enrichment and coupling of the finite element and meshless methods. Int. J. Numer. Methods Engrg. 48 (2000) 1615-1636
29. Hegen D. Element free Galerkin methods in combination with finite element approaches. Comput. Methods Appl. Mech. Engrg. 135 (1996) 143-166
30. Liu W.K., Uras R.A., and Chen Y. Enrichment of the finite element method with reproducing kernel particle method. J. Appl. Mech. 64 (1997) 861-870
31. Xikui Li, Qinglin Duan, Xianhong Han, D.C. Sheng, Adaptive coupled arbitrary Lagrangian-Eulerian finite element and meshfree method for injection molding process, Int. J. Numer. Methods Engrg., in press, doi:10.1002/nme.2117.
32. Chorin A.J. Numerical solution of the Navier-Stokes equations. Math. Comput. 22 (1968) 742-762
33. Chorin A.J. On the convergence of discrete approximation to the Navier-Stokes equations. Math. Comput. 23 (1969) 341-353
34. Temam R. Sur 1' approximation de la solution deséquations de Navier-Stokes par la méthode des pas fractionnaries II. Arch. Rat. Mech. Anal. 33 (1969) 377-385
35. Comini G., and Del Guidice S. Finite element solution of incompressible Navier-Stokes equations. Numer. Heat Transfer, Part A 5 (1972) 463-478
36. Donea J., Giuliani S., Laval H., and 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
37. Hughes T.J.R. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Comput. Methods Appl. Mech. Engrg. 127 (1995) 387-401
38. Li X., Han X., and Pastor M. An iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3845-3859
39. Li X., and Han X. An iterative stabilized fractional step algorithm for numerical solution of incompressible N-S equations. Int. J. Numer. Methods Fluids 49 (2005) 395-416
40. Han X.H., and Li X.K. A free surface tracking and mesh generation scheme for the injection molding process. J. Dalian Univ. Technol. 45 (2005) 633-639 (in Chinese)
41. Bell B.C., and Surana K.S. p-Version least squares finite element formulation for two-dimensional incompressible Newtonian and non-Newtonian non-isothermal fluid flow. Comput. Struct. 54 (1995) 83-96
42. Douglas C., and Roylance D. Finite Element Flow Analysis (1982), North-Holland, New York
43. Han X., and Li X. An iterative stabilized CNBS-CG scheme for incompressible non-isothermal non-Newtonian fluid flow. Int. J. Heat Mass Transfer 50 (2007) 847-856
44. Nassehi V. Practical Aspects of Finite Element Modelling of Polymer Processing (2001), Wiley
45. Silliman W.J., and Scriven L.E. Separating flow near a static contact line: slip at a wall and shape of a free surface. J. Comput. Phys. 34 (1980) 287-313