This paper deals with the solution of two-dimensional fluid flow problems using the truly meshless Local Petrov-Galerkin (MLPG) method. The present method is a truly meshless method based only on a number of randomly located nodes. Radial basis functions (RBF) are employed for constructing trial functions in the local weighted meshless local Petrov-Galerkin method for two-dimensional transient viscous fluid flow problems. No boundary integration is needed, no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions due to satisfaction of kronecker delta property in RBFs. Three different radial basis functions (RBFs), i.e. Multiquadrics (MQ), Gaussian (EXP) and Thin Plate Splines (TPS) are examined and the selection of their shape parameters is studied based on closed-form solutions. The effect of quadrature domain size is also studied. The variational method is used for the development of discrete equations. The results are obtained for a two-dimensional model problem using three RBFs and compared with the results of finite element and exact methods. Results show that the proposed method is highly accurate and possesses no numerical difficulties.
Skip Nav Destination
ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering
July 17–20, 2006
Miami, Florida, USA
Conference Sponsors:
- Fluids Engineering Division
ISBN:
0-7918-4750-0
PROCEEDINGS PAPER
Meshless Solution of 2D Fluid Flow Problems by Subdomain Variational Method Using MLPG Method With Radial Basis Functions (RBFs)
Mohammad Haji Mohammadi,
Mohammad Haji Mohammadi
Sharif University of Technology, Tehran, Iran
Search for other works by this author on:
A. Shamsai
A. Shamsai
Sharif University of Technology, Tehran, Iran
Search for other works by this author on:
Mohammad Haji Mohammadi
Sharif University of Technology, Tehran, Iran
A. Shamsai
Sharif University of Technology, Tehran, Iran
Paper No:
FEDSM2006-98286, pp. 333-341; 9 pages
Published Online:
September 5, 2008
Citation
Haji Mohammadi, M, & Shamsai, A. "Meshless Solution of 2D Fluid Flow Problems by Subdomain Variational Method Using MLPG Method With Radial Basis Functions (RBFs)." Proceedings of the ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. Volume 1: Symposia, Parts A and B. Miami, Florida, USA. July 17–20, 2006. pp. 333-341. ASME. https://doi.org/10.1115/FEDSM2006-98286
Download citation file:
2
Views
0
Citations
Related Proceedings Papers
Related Articles
Discussion: “Shear Coefficients for Timoshenko Beam Theory” (Hutchinson, J. R., 2001, ASME J. Appl. Mech., 68 , pp. 87–92)
J. Appl. Mech (November,2001)
Closure to “On Shear Coefficients for Timoshenko Beam Theory” (2001, ASME J. Appl. Mech., 68 , p. 959)
J. Appl. Mech (November,2001)
Some Further Remarks on Hamilton’s Principle
J. Appl. Mech (January,2011)
Related Chapters
Variational Methods
Vibrations of Linear Piezostructures
Static Deformations Budget
Mechanics of Accuracy in Engineering Design of Machines and Robots Volume II: Stiffness and Metrology
Fluid Mechanics
Engineering Practice with Oilfield and Drilling Applications