Open Access

ARTICLE

Local Moving Least Square - One-Dimensional IRBFN Technique: Part II- Unsteady Incompressible Viscous Flows

D. Ngo-Cong^1,2, N. Mai-Duy¹, W. Karunasena², T. Tran-Cong^1,3

1 Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia.
2 Centre of Excellence in Engineered Fibre Composites, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia.
3 Corresponding author, Email: trancong@usq.edu.au.

Computer Modeling in Engineering & Sciences 2012, 83(3), 311-352. https://doi.org/10.3970/cmes.2012.083.311

Abstract

In this study, local moving least square - one dimensional integrated radial basis function network (LMLS-1D-IRBFN) method is presented and demonstrated with the solution of time-dependent problems such as Burgers' equation, unsteady flow past a square cylinder in a horizontal channel and unsteady flow past a circular cylinder. The present method makes use of the partition of unity concept to combine the moving least square (MLS) and one-dimensional integrated radial basis function network (1D-IRBFN) techniques in a new approach. This approach offers the same order of accuracy as its global counterpart, the 1D-IRBFN method, while the system matrix is more sparse than that of the 1D-IRBFN, which helps reduce the computational cost significantly. For fluid flow problems, the diffusion terms are discretised by using LMLS-1D-IRBFN method, while the convection terms are explicitly calculated by using 1D-IRBFN method. The present numerical procedure is combined with a domain decomposition technique to handle large-scale problems. The numerical results obtained are in good agreement with other published results in the literature.

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Keywords

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