Application of Meshless Local Petrov-Galerkin (MLPG) Approach to Simulation of Incompressible Flow

REFERENCES

• 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 . [CSA]
   Web of Science ®Google Scholar
• 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 . [CSA]
   Web of Science ®Google Scholar
• 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. [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• 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 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• 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 . [CSA] [CROSSREF]
   Google Scholar
• T. Belytschko , Y. Y. Lu , and L. Gu , Element-Free Galerkin Methods , Int. J. Numer. Meth. Eng. , vol. 37 , pp. 229 – 256 , 1994 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• 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 .
   Google Scholar
• G. R. Liu and Y. T. Gu , A Point Interpolation Method , Proc. 4th Asia-Pacific Conf. on Computational Mechanics , Singapore , pp. 1009 – 1014 , 1999 .
   Google Scholar
• 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 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• 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 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• 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 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• 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 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• 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 . [CSA]
   Web of Science ®Google Scholar
• 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 . [CSA]
   Web of Science ®Google Scholar
• 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 .
   Google Scholar
• 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 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• G. R. Liu , Mesh Free Methods: Moving Beyond the Finite Element Method , CRC Press , BOCA Raton , FL , 2002 .
   Google Scholar
• Y. X. Mukherjee and S. Muknherjee , Boundary Node Method for Potential Problems , Int. J. Numer. Meth. Eng. , vol. 40 , pp. 797 – 815 , 1997 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• 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 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• 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 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• M. Kawahara , N. Yoshimura , and K. Nakagawa , Analysis of Steady Incompressible Viscous Flow , in et al. ., Finite Element Methods in Flow Problems , pp. 107 – 120 , UAH Press , Huntsville , Alabama , 1974 .
   Google Scholar
• 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 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• 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. [CSA]
   Web of Science ®Google Scholar
• 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 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar