Open Access

ARTICLE

Galerkin/Collocation Methods Based on 1D-Integrated-RBFNs for Viscoelastic Flows

by D. Ho-Minh¹, N. Mai-Duy¹, T. Tran-Cong¹

1 Computational Engineering and Science Research Centre (CESRC), Faculty of Engineering and Surveying (FoES), The University of Southern Queensland, Toowoomba, QLD 4350, Australia.

Computer Modeling in Engineering & Sciences 2010, 70(3), 217-252. https://doi.org/10.3970/cmes.2010.070.217

Abstract

In this paper, one-dimensional integrated radial-basis-function networks (1D-IRBFNs) are introduced into the Galerkin and point-collocation formulations to simulate viscoelastic flows. The computational domain is represented by a Cartesian grid and IRBFNs, which are constructed through integration, are employed on each grid line to approximate the field variables including stresses in the streamfunction-vorticity formulation. Two types of fluid, namely Oldroyd-B and CEF models, are considered. The proposed methods are validated through the numerical simulation of several benchmark test problems including flows in a rectangular duct and in a corrugated tube. Numerical results show that accurate results are obtained using relatively-coarse grids.

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