A Meshfree Solution of Tow-Dimensional Potential Flow Problems
In this paper, mesh-free element free Galerkin (EFG) method is extended to solve two-dimensional potential flow problems. Two ideal fluid flow problems (i.e. flow over a rigid cylinder and flow over a sphere) have been formulated using variational approach. Penalty and Lagrange multiplier techniques have been utilized for the enforcement of essential boundary conditions. Four point Gauss quadrature have been used for the integration on two-dimensional domain (Ω) and nodal integration scheme has been used to enforce the essential boundary conditions on the edges (┌). The results obtained by EFG method are compared with those obtained by finite element method. The effects of scaling and penalty parameters on EFG results have also been discussed in detail.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1055271Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1319
 H. Lin, and S. N. Atluri, "The meshless local Petrov Galerkin (MLPG) method for solving incompressible Navier-Strokes equation," Comp. Modeling Eng. Sci., vol. 2, pp. 117-142, 2001.
 H. Lin, and S. N. Atluri, "Meshless local Petrov Galerkin (MLPG) method for convection-diffusion Problems," Comp. Modeling Eng. Sci., vol. 1, pp. 45-60, 2000.
 E. Onate, and S. Idelsohn, "A mesh-free point method for advectivediffusive transport and fluid flow problems," Comput. Methods, vol. 21, pp. 283-292, 1998.
 E. Onate, S. Idelsohn, O. C. Zienkiewicz, R. L. Taylor, and C. Sacco, "A stabilized finite point method for analysis of fluid mechanics problems," Comp. Methods Appl. Mech. Eng., vol. 139, pp. 315-346, 1996.
 R. Löhner, C. Sacco, E. Onate, and S. Idelsohn, "A finite point method for compressible flow," Int. J. Numer. Methods Eng., vol. 53, pp. 1765- 1779, 2002.
 T. Sophy, and H. Sadat, "A meshless formulation for three dimensional laminar natural convection," Numer. Heat Transfer, vol. 41, pp. 433- 445, 2002.
 W. K. Liu, S. Jun, D. T. Sihling, Y. Chen, and W. Hao, "Multiresolution reproducing kernel paticle method for computational fluid dynamics," Int. J. Numer. Methods Fluids, vol. 24, pp. 1391-1415, 1997.
 Y. C. Hon, S. Li, and M. Huang, "A meshless computational method for the shear flow of Johnson-Segalman fluid," Int. J. Comput. Methods Eng. Mech., vol. 6, pp. 59-64, 2005.
 I. Tsukanov, V. Shapiro, and S. Zhang, "A meshfree method for incompressible fluid dynamics problems," Int. J. Numer. Methods Eng., 58, pp. 127-158, 2003.
 T. Chen, and I. S. Raju, "A coupled finite element and meshless local Petrov-Galerkin method for two-dimensional potential problems," Comp. Methods Appl. Mech. Eng., vol. 192, pp. 4533-4550, 2003.
 M. Cheng, and G. R. Liu, "A noval finite point method for flow simulation," Int. J. Numer. Methods Fluids, vol. 39, pp. 1161-1178, 2002.
 I. V. Singh, "Application of meshless EFG method in fluid flow problems," Sadhana, vol. 29, pp. 285-296, 2004.
 C. Du, "An element free Galerkin method for simulation of stationary two-dimensional shallow water flows in river," Comp. Methods Appl. Mech. Eng., vol. 182, pp. 89-107, 2000.
 S. L. L. Veradi, J. M. Machado, and J. R. Cardoso, "The element-free Galerkin method applied to the study of fully developed magnetohydrodynamic duct flows," IEEE Trans. Magnetics, vol. 38, pp. 941-944, 2002.
 I. V. Singh, K. Sandeep, and R. Prakash, "Heat transfer analysis of twodimensional fins using meshless element-free Galerkin method," Numer. Heat Transfer, vol. 44, pp. 73-84, 2003.
 T. J. Chung, Finite Element Analysis in Fluid Dynamics, McGraw-Hill: USA, 1978, pp. 170-202.