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ARTICLE

High-Order Upwind Methods Based on C²-Continuous Two-Node Integrated-RBF Elements for Viscous Flows

D.-A. An-Vo¹, N. Mai-Duy¹, T. Tran-Cong¹

1 Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia

Computer Modeling in Engineering & Sciences 2011, 80(2), 141-178. https://doi.org/10.3970/cmes.2011.080.141

Abstract

In this paper, 2-node integrated radial basis function elements (IRBFEs) [CMES, vol.72, no.4, pp.299-334, 2011] are further developed for the simulation of incompressible viscous flows in two dimensions. Emphasis is placed on (i) the incorporation of C²-continuous 2-node IRBFEs into the subregion and point collocation frameworks for the discretisation of the stream function-vorticity formulation on Cartesian grids; and (ii) the development of high order upwind schemes based on 2-node IRBFEs for the case of convection-dominant flows. High levels of accuracy and efficiency of the present methods are demonstrated by solutions of several benchmark problems defined on rectangular and non-rectangular domains.

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