Parallel meshless EFG solution for fluid flow problems

Numerical Heat Transfer, Part B: Fundamentals

Volumn 48, Issue 1, 2005, Pages 45-66

  Singh, I V ^a   Jain, P K ^a  

^a BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL GEOMETRY; CRACK PROPAGATION; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; LEAST SQUARES APPROXIMATIONS; PARALLEL ALGORITHMS; PROBLEM SOLVING;

DIFFUSE-ELEMENT METHOD; FINITE ELEMENT EQUATIONS; MOVING LEAST-SQUARES (MLS); SMOOTH PARTICLE HYDRODYNAMICS (SPH);

FLOW OF FLUIDS;

EID: 22444436414     PISSN: 10407790     EISSN: None     Source Type: Journal    
DOI: 10.1080/10407790590935993     Document Type: Article

References (32)

1. J. J. Monaghan, An Introduction to SPH, Comput. Phys. Commun., vol. 48, pp. 89-96, 1988.
2. B. Nayroles, G. Touzot, and P. Villon, Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Elements, Comput. Mech., vol. 10, pp. 307-318, 1992.
3. T. Belytschko, Y. Y. Lu, and L. Gu, Element Free Galerkin Methods, Int. J. Numer. Meth. Eng., vol. 37, pp. 229-256, 1994.
4. W. K. Liu, S. Jun, and Y. F. Zhang, Reproducing Kernel Particle Methods, Int. J. Numer. Meth. Eng., vol. 20, pp. 1081-1106, 1995.
5. I. Babuska and J. M. Melenk, The Partition of Unity Method, Int. J. Numer. Meth. Eng., vol. 40, pp. 727-758, 1997.
6. C. A. Durate and J. T. Oden, An H-p Adaptive Method Using Clouds, Comput. Meth. Appl. Mech. Eng., vol. 139, pp. 237-262, 1996.
7. G. Yagawa and T. Yamada, Free Mesh Method, A New Meshless Finite Element Method, Comput. Mech., vol. 18, pp. 383-386, 1996.
8. N. Sukumar, B. Moran, and T. Belytschko, The Natural Element Method in Solid Mechanics, Int. J. Numer. Meth. Eng., vol. 43, pp. 839-887, 1998.
9. T. Zhu, J. D. Zhang, and S. N. Atluri, A Meshless Local Boundary Integral Equation (LBIE) Method for Solving Nonlinear Problems, Comput. Mech., vol. 22, pp. 174-186, 1998.
10. S. N. Atluri and T. Zhu, A New Meshless Local Petrov-Galerkin (MLPG) Approach in Computational Mechanics, Comput. Mech., vol. 22, pp. 117-127, 1998.
11. S. De and K. J. Bathe, The Method of Finite Spheres, Comput. Mech., vol. 25, pp. 329-345, 2000.
12. G. R. Liu and Y. T. Gu, A Local Radial Point Interpolation Method (LRPIM) for Free Vibration Analysis of 2-D Solids, J. Sound Vibration, vol. 246, no. 1, pp. 29-46, 2001.
13. J. Zhang, Z. Yao, and M. Tanaka, The Meshless Regular Hybrid Boundary Node Method for 2-D Linear Elasticity, Eng. Anal. Bound. Elem., vol. 27, pp. 259-268, 2003.
14. M. Shirazaki and G. Yagawa, Large-Scale Parallel Flow Analysis Based on Free Mesh Method: A Virtually Meshless Method, Comput. Meth. Appl. Mech. Eng., vol. 174, pp. 419-431, 1999.
15. D. F. Medina and J. K. Chen, Three-Dimensional Simulations of Impact Induced Damage in Composite Structures Using the Parallelized SPH Method, Composites A, vol. 31, pp. 853-860, 2000.
16. M. Griebel and M. A. Schweitzer, A Particle-Partition of Unity Method-Part IV: Parallelization, Mesh-Free Methods for Partial Differential Equations, Lecture Notes Comput. Sci. Eng., vol. 26, pp. 161-192, 2002.
17. N. Sukumar, B. Moran, T. Black, and T. Belytschko, An Element-Free Galerkin Method for Three-Dimensional Fracture Mechanics, Comput. Mech., vol. 20, pp. 170-175, 1997.
18. T. Belytschko, Y. Y. Lu, L. Gu, and M. Tabbara, Element-Free Galerkin Methods for Static and Dynamic Fracture, Int. J. Solids Struct., vol. 32, pp. 2547-2570, 1995.
19. Y. Y. Lu, T. Belytschko, and M. Tabbara, Element-Free Galerkin Methods for Wave Propagation and Dynamic Fracture, Comput. Meth. Appl. Mech. Eng., vol. 126, pp. 131-153, 1995.
20. T. Belytschko, Y. Y. Lu, and L. Gu, Crack Propagation by Element-Free Galerkin Methods, Eng. Fracture Mech., vol. 51, pp. 295-315, 1995.
21. P. Krysl and T. Belytschko, Analysis of Thin Plates by Element-Free Galerkin Method, Comput. Mech., vol. 17, pp. 26-35, 1996.
22. P. Krysl and T. Belytschko, Analysis of Thin Shells by Element-Free Galerkin Method, Int. J. Solids Struct., vol. 33, pp. 3057-3080, 1996.
23. X. L. Chen, G. R. Liu, and S. P. Lim, An Element Free Galerkin Method for the Free Vibration Analysis of Composite Laminates of Complicated Shape, Composite Struct., vol. 59, pp. 279-289, 2003.
24. Y. Haitian and L. Yan, A Combined Approach of EFGM and Precise Algorithm in Time Domain Solving Viscoelasticity Problems, Int. J. Solids Struct., vol. 40, pp. 701-714, 2003.
25. V. Cingoski, N. Miyamoto, and H. Yamashita, Element-Free Galerkin Method for Electromagnetic Field Computations, IEEE Trans. Magnetism, vol. 34, pp. 3236-3239, 1998.
26. I. V. Singh, K. Sandeep, and R. Prakash, The Element Free Galerkin Method in Three-Dimensional Steady State Heat Conduction, Int. J. Comput. Eng. Sci., vol. 3, no. 3, pp. 291-303, 2002.
27. I. V. Singh, K. Sandeep, and R. Prakash, Heat Transfer Analysis of Two-Dimensional Fins Using Meshless Element-Free Galerkin Method, Numer. Heat Transfer A, vol. 44, pp. 73-84, 2003.
28. Ph. Bouillard and S. Suleau, Element-Free Galerkin Solutions for Helmholtz Problems: Formulation and Numerical Assessment of the Pollution Effect, Comput. Meth. Appl. Mech. Eng., vol. 162, pp. 317-335, 1998.
29. Y. Y. Lu, T. Belytschko, and L. Gu, A New Implementation of the Element Element-Free Galerkin Method, Comput. Meth. Appl. Mech. Eng., vol. 113, pp. 397-414, 1994.
30. J. Dolbow and T. Belytschko, An Introduction to Programming the Meshless Element Free Galerkin Method, Arch. Comput. Meth. Eng., vol. 43, pp. 785-819, 1998.
31. T. Belytschko, Y. Krongauz, M. Fleming, D. Organ, and W. K. Liu, Smoothing and Accelerated Computations in Element-Free Galerkin Method, J. Comput. Appl. Math., vol. 74, pp. 111-126, 1996.
32. T. Belytschko, Y. Krongauz, D. J. Organ, M. Fleming, and P. Krysl, Meshless Methods: An Overview and Recent Developments, Comput. Meth. Appl. Mech. Eng., vol. 139, pp. 3-47, 1996.