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.
- Fluids Engineering Division
Meshless Solution of 2D Fluid Flow Problems by Subdomain Variational Method Using MLPG Method With Radial Basis Functions (RBFs)
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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
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