Application of meshless local Petrov-Galerkin (MLPG) approach to simulation of incompressible flow

Numerical Heat Transfer, Part B: Fundamentals

Volumn 48, Issue 5, 2005, Pages 459-475

  Wu, Y L ^a   Liu, G R ^a   Gu, Y T ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; LEAST SQUARES APPROXIMATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

GLOBAL MESH; MLPG METHOD; NODAL DISTRIBUTION;

HEAT TRANSFER;

EID: 27744487625     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/10407790500324763     Document Type: Article

References (24)

1. I. V. Singh, Meshless EFG Method in Three-Dimensional Heat Transfer Problems: A Numerical Comparison, Cost and Error Analysis, Numer. Heat Transfer A, vol. 46, no. 2, pp. 199-220, 2004.
2. Y. Liu, X. Zhang, and M. W. Lu, A Meshless Method Based on Least-Squares Approach for Steady- and Unsteady-State Heat Conduction Problems, Numer. Heat Transfer B, vol. 47, no. 3, pp. 257-275, 2005.
3. H. T. Yang and L. Liu, Solving Transient Heat Conduction Problems with Cyclic Symmetry via a Paralleled EFGM and a Precise Algorithm, Numer. Heat Transfer B, vol. 46, no. 5, pp. 479-495, 2004.
4. T. Sophy, H. Sadat, and C. Prax, A Meshless Formulation for Three- Dimensional Laminar Natural Convection, Numer. Heat Transfer B, vol. 41, no. 5, pp. 433-445, 2002.
5. 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.
6. T. Belytschko, Y. Y. Lu, and L. Gu, Element-Free Galerkin Methods, Int. J. Numer. Meth. Eng., vol. 37, pp. 229-256, 1994.
7. J. M. Melenk and I. Babuska, The Partition of Unity Finite Element Method: Basic Theory and Applications, TICAM Rep. 96-01, University of Texas at Austin, Austin, TX, 1996.
8. G. R. Liu and Y. T. Gu, A Point Interpolation Method, Proc. 4th Asia-Pacific Conf. on Computational Mechanics, Singapore, pp. 1009-1014, 1999.
9. G. R. Liu and Y. T. Gu, A Local Radial Point Interpolation Method (LRPIM) for Free Vibration Analyses of 2-D Solids, J. Sound Vibration, vol. 246, no. 1, pp. 29-46, 2001.
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. G. R. Liu and Y. T. Gu, Meshless Local Petrov-Galerkin (MLPG) Method in Combination with Finite Element and Boundary Element Approaches, Comput. Mech., vol. 26, no. 6, pp. 536-546, 2000.
12. Y. T. Gu and G. R. Liu, A Meshless Local Petrov-Galerkin (MLPG) Method for Free and Forced Vibration Analyses for Solids, Comput. Mech., vol. 27, no. 3, pp. 188-198, 2001.
13. Y. T. Gu and G. R. Liu, A Meshless Local Petrov-Galerkin (MLPG) Formulation for Static and Free Vibration Analyses of Thin Plates, Comput. Modeling Eng. Sci., vol. 2, no. 4, pp. 463-476, 2002.
14. H. Lin and S. N. Atluri, The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations, Comput. Modeling Eng. Sci., vol. 2, no. 2, pp. 117-142, 2001.
15. G. R. Liu, Y. L. Wu, and Y. T. Gu, Application of Meshless Local Petrov-Galerkin (MLPG) Approach to Fluid Flow Problem, APCOM'01, Sydney, Australia, November 2001.
16. T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, and P. Krysl, Meshless Methods: An Overview and Recent Developments, Comput. Meth. Appl. Mech. Eng., vol. 139, pp. 3-47, 1996.
17. G. R. Liu, Mesh Free Methods: Moving Beyond the Finite Element Method, CRC Press, BOCA Raton, FL, 2002.
18. Y. X. Mukherjee and S. Muknherjee, Boundary Node Method for Potential Problems, Int. J. Numer. Meth. Eng., vol. 40, pp. 797-815, 1997.
19. S. N. Atluri, H. G. Kim, and J. Y. Cho, A Critical Assessment of the Truly Meshless Local Petrov-Galerkin (MLPG) and Local Boundary Integral Equation (LBIE) Methods, Comput. Mech., vol. 24, pp. 348-372, 1999.
20. Y. L. Wu and G. R. Liu, A Meshfree Formulation of Local Radial Point Interpolation Method (LRPIM) for Incompressible Flow Simulation, Comput. Mech., vol. 30, nos. 5-6, pp. 355-365, 2003.
21. M. Kawahara, N. Yoshimura, and K. Nakagawa, Analysis of Steady Incompressible Viscous Flow, in J. T. Oden, et al., Finite Element Methods in Flow Problems, pp. 107-120, UAH Press, Huntsville, Alabama, 1974.
22. C. Shu, Application of Differential Quadrature Method to Simulate Natural Convection in a Concentric Annulus, Int. J. Numer. Meth. Fluids, vol. 30, pp. 977-993, 1999.
23. F. Moukalled and S. Acharya, Natural Convection in the Annulus between Concentric Horizontal Circular and Square Cylinders, J. Thermophys. Heat Transfer, vol. 10, no. 3, pp. 524-531, 1996.
24. C. Shu, H. Xue, and Y. D. Zhu, Numerical Study of Natural Convection in an Eccentric Annulus between a Square Outer Cylinder and a Circular Inner Cylinder Using DQ Method, Int. J. Heat Mass Transfer, vol. 44, pp. 3321-3333, 2001.