Adaptive mesh generation for fluid mechanics problems

International Journal for Numerical Methods in Engineering

Volumn 47, Issue 1-3, 2000, Pages 629-662

  Nithiarasu, P ^a   Zienkiewicz, O C ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Adaptive remeshing; Curvature; FEM; Fluid mechanics; Gradient; L2 norm

Indexed keywords

COMPUTATIONAL GEOMETRY; ERROR ANALYSIS; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; INTERPOLATION;

ADAPTIVE MESH GENERATION; COMPRESSIBLE FLOW;

COMPUTATIONAL FLUID DYNAMICS;

FINITE ELEMENT METHOD; FLUID MECHANICS;

EID: 0034628098     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<629::AID-NME786>3.0.CO;2-Y     Document Type: Article

References (56)

1. Zienkiewicz OC, Zhu JZ. A simple error estimator and adaptive procedure for practical engineering analysis. International Journal for Numerical Methods in Engineering 1987; 24:337-357.
2. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates, Part 1: the recovery technique, International Journal for Numerical Methods in Engineering 1992; 33:1331-1364.
3. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates, Part 2, International Journal for Numerical Methods in Engineering 1992; 33:1365-1382.
4. Babuska I, Rheinboldt WC. Error estimates for adaptive finite element computation. SIAM Journal of Numerical Analysis 1978; 18:736-754.
5. Peraire J, Vahdati M, Morgan K, Zienkiewicz OC. Adaptive remeshing for compressible flow computations. Journal of Computational Physics 1987; 72:449-466.
6. Zhu JZ, Hinton E, Zienkiewicz OC. Mesh enrichment against mesh regeneration using quadrilateral elements. Communications in Numerical Methods in Engineering 1993; 9:547-554.
7. Zienkiewicz OC, Wu J. Automatic directional refinement in adaptive analysis of compressible flows. International Journal for Numerical Methods in Engineering 1994; 37:2189-2210.
8. Zienkiewicz OC, Huang M, Pastor M. Localization problems in plasticity using finite elements with adaptive remeshing. International Journal for Numerical Methods in Engineering 1995; 19;127-148.
9. Zienkiewicz OC, Morgan K, Peraire J, Zhu JZ. Some expanding horizons for computational mechanics - error estimates, mesh generation and hyperbolic problems. Computational mechanics - Advances and Trends, ASME Meeting, Anaheim, CA, 7-12, December 1986; 281-297.
10. Löhner R. Adaptive remeshing for transient problems. Computer Methods in Applied Mechanics and Engineering 1989; 75:195, 214.
11. Löhner R. Morgan K. Zienkiewicz OC. Adaptive grid refinement for the Eular and compressible Navier-Stokes equations. In Accuracy Estimates and Adaptive Refinement in Finite Element Computations, Chapter 15, Babuska I, Zienkiewicz OC, Gago J, Oliveira ER de A (eds). Wiley: New York, 1986; 281-298.
12. Löhner R, Morgan K, Zienkiewicz OC. An adaptive finite element procedure for compressible high speed flows. Computer Methods in Applied Mechanics and Engineering 1985; 51:441-465.
13. Morgan K, Peraire J, Peiro J, Zienkiewicz OC. Adaptive remeshing applied to the solution of a shock interaction problem on a cylindrical leading edge. In Computational Methods in Aeronautical Fluid Dynamics, Stow P (ed.). Clarenden Press: Oxford, 1990; 327-344.
14. Peraire J, Morgan K, Peiro J, Zienkiewicz OC. An adaptive finite element method for high speed flows. AIAA 25th Aerospace Sciences Meeting, January, Reno, Nevada. AIAA-87-0558.
15. Zienkiewicz OC, Pastor M, Huang M. Softening, Localization and adaptive remeshing, capture of discontinuous solutions. Computational Mechanics 1995; 17:98-106.
16. Hassan O, Morgan K, Peraire J, Probert EJ, Thareja RR. Adaptive unstructured mesh methods for steady viscous flow. AIAA Paper, 1991.
17. Hassan O, Probert EJ, Morgan K, Peraire J. Mesh generation and adaptivity for the solution of compressible viscous high speed flows. International Journal for Numerical Methods in Engineering 1995; 38:1123-1148.
18. Hassan O, Morgan K, Probert EJ, Peraire J. Unstructured tetrahedral mesh generation for three dimensional viscous flows. International Journal for Numerical Methods in Engineering 1996; 39:549-567.
19. Palmerio B. A two-dimensional FEM adaptive moving-node method for steady Euler flow simulation. Computer Methods in Applied Mechanics and Engineering 1988; 71:315-340.
20. Yahia DDD, Habashi WG, Tam A, Vallet MG, Fortin M. A directionally adaptive methodology using an edge based error estimate on quadrilateral grids. International Journal for Numerical Methods in Fluids 1996; 23:673-690.
21. Fortin M, Vallet M-G, Dompierre J, Bourgault Y, Habashi WG. Anistropic mesh adaption: theory, validation and applications. Computational Fluid Dynamics 1996; 174-180.
22. Castro-Diaz MJ, Borouchaki H, George PL, Hecht F, Mohammadi B. Error interpolation minimization and anisptropic mesh generation. Proceedings of the International Conference Finite Elements Fluids - New Trends Applications, Venezia, 15-21 October 1995; 1139-1148.
23. Fortin M, Vallet MG, Dompierre J, Bourgault Y, Habashi WG. Anisotropic mesh adaption: theory, validation and applications. Computational Fluid Dynamics 1996; 174-180.
24. Castro-Diaz MJ, Borouchaki H, George PL, Hecht F, Mohammadi B. Anisotropic adaptive mesh generation in two dimensions for CFD. Computational Fluid Dynamics 1996; 181-186.
25. Borouchaki H, George PL, Hecht F, Laug P, Saltel E. Delaunay mesh generation governed by metric specifications. Part I. Algorithms. Finite Elements Analysis Design 1997; 25:61-83.
26. Borouchaki H, George PL, Mohammadi B. Delaunay mesh generation governed by metric specifications, Part II. Applications. Finite Elements Analysis Design 1997; 25:85-109.
27. Jiang BN, Garey GF. Adaptive refinement for least-square finite elements with element by element conjugate gradient solution. International Journal for Numerical Methods in Engineering 1987; 24:596-580.
28. Demkowicz L, Oden JT, Rachowicz W, Hardy O. Toward a universal h-p adaptive finite element strategy, Part 1. Constrained approximation and data structure. Computer Methods in Applied Mechanics and Engineering 1989: 77:79-112.
29. Oden JT, Demkowicz L, Rachowicz W, Westermann TA. Toward a universal h-p adaptive finite element strategy, Part 2. A posteriori error estimation. Computer Methods in Applied Mechanics and Engineering 1989; 77:113-180.
30. Demokowicz L, Oden JT, Rachowicz W. A new finite element methods for solving compressible Navier-Stokes equations based on an operator splitting method and h-p adaptivity. Computer Methods in Applied Mechanics and Engineering 1990; 84:275-326.
31. Oden JT, Wu W, Ainsworth M. An a posteriori error estimate for finite element approximations of the Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1994; 111:185-202.
32. Oden JT, Wu W, Legat V. An hp adaptive strategy for finite element approximations of the Navier-Stokes equations. International Journal for Numerical Methods in Fluids 1995; 20:831-851.
33. Jin H, Prudhomme S. A posteriori error estimation of steady-state finite element solution of the Navier-Stokes equations by a subdomain residual method. Computer Methods in Applied Mechanics and Engineering 1998; 159: 19-48.
34. Wu J, Zhu JZ, Szmelter J, Zienkiewicz OC. Error estimation and adaptivity in Navier-Stokes incompressible flows. Computational Mechanics 1991; 61:30-39.
35. Hetu JF, Pelletier DH. Adaptive remeshing for viscous incompressible flows. AIAA Journal 1992; 30:1986-1992.
36. Hetu JF, Pelletier H. Fast, adaptive finite element scheme for viscous incompressible flows. AIAA Journal 1992; 30:2677-2682.
37. Pelletier D, Ilinca F. Adaptive finite element method for mixed convection. Journal of Thermodynamics and Heat Transfer 1995; 9:708-714.
38. Ilinca F, Pelletier D, Garon A. An adaptive finite element method for two-equation turbulence model in wall bounded flows. International Journal for Numerical Methods in Fluids 1997; 24:101-120.
39. Ilinca F, Pelletier D, ArnouxGuisse F. An adaptive finite element scheme for turbulence free shear flows. International Journal of Computational Fluid Dynamics 1997; 8:171-188.
40. Pelletier D, Ignat L, Ilinca F. Adaptive finite element method for conjugate heat transfer. Numerical Heat Transfer Part A, Applications 1997; 32:267-287.
41. Pelletier D, Ilinca F, Turgeon E. An adaptive finite element method for forced convection. International Journal for Numerical Methods in Fluids 1997; 25:803-823.
42. de Sampaio PAB, Lyra PRM, Morgan K, Weatherill NP. Petrov-Galerkin solution of the incompressible Navier-Stokes equations in primitive variables with adaptive remeshing. Computer Methods in Applied Mechanics and Engineering 1993; 106:143-178.
43. Rachowicz W. An anisotropic h-adaptive finite element method for compressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1997; 146:231-252.
44. Rachowicz W. An anisotropic h-type mesh refinement strategy. Computer Methods in Applied Mechanics and Engineering 1993; 109:169-181.
45. Zienkiewicz OC, Taylor RL. The finite Element Method (4th edn), vol 2. McGraw-Hill Book Company: New York, 1991.
46. Zienkiewicz OC, Codina R. A general algorithm for compressible and incompressible flow. Part I. The split characteristic based scheme. Interntional Journal for Numerical Methods in Fluids 1995; 20:869-885.
47. Zienkiewicz OC, Morgan K, Satya Sai BVK, Codina R, Vázquez. A general algorithm for compressible and incompressible flow - Part II. Tests on the explicit form. International Journal for Numerical Methods in Fluids 1995; 20:887-913.
48. Codina R, Vázquez M, Zienkiewicz OC. General algorithm for compressible and incompressible flows, Part III - A semi-implicit form. International Journal for Numerical Methods in Fluids 1998; 27:13-32.
49. Zienkiewicz OC, Nithiarasu P, Codina R, Vázquez M, Ortiz P. An efficient and accurate algorithm for fluid mechanics problems. The characteristic based split (CBS) procedure. International Journal for Numerical Methods in Fluids 1999, to appear.
50. Nithiarasu P, Zienkiewicz OC, Satya Sai BVK, Morgan K, Codina R, Vázquez. Shock capturing viscosities for the general fluid mechanics algorithm. International Journal for Numerical Methods in Fluids 1998; 28(9):1325-1353.
51. Ghia U, Ghia KN, Shin CT. High-resolution for incompressible flow using the Navier-Stokes equations and multigrid method. Journal of Computational Physics 1982; 48:387-411.
52. Denham MK, Patrick MA. Laminar flow over a downstream racing step in a two dimensional channel. Transactions of the Institute of Chemical Engineers 1974; 52:361-367.
53. de Vahl Davis G. Natural convection of air in a square cavity: a bench mark numerical solution. International Journal for Numerical Methods in Fluids 1983; 3:249-264.
54. Massaroatti N, Nithirasu P, Zienkiewicz OC. Characteristic-Based-Split (CBS) Algorithm for incompressible flow problems with heat transfer. International Journal of Numerical Methods for Heat and Fluid Flow 1998; 8: 969-990.
55. Ramaswamy B, Jue TC, Akin JE. Semi-implicit and explicit finite element schemes for coupled fluid/thermal problems. International Journal for Numerical Methods in Engineering 1992; 34:675-696.
56. Nithiarasu P, Seetharamu KN, Sundararajan T. Finite element analysis of transient natural convection in an odd-shapped enclosure. International Journal of Numerical Methods for Heat and Fluid Flow 1998; 8:199-216.