A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems

Abstract

Radial basis function networks (RBFNs) have been widely used in solving partial differential equations as they are able to provide fast convergence. Integrated RBFNs have the ability to avoid the problem of reduced convergence-rate caused by differentiation. This paper is concerned with the use of integrated RBFNs in the context of control-volume discretisations for the simulation of fluid-flow problems. Special attention is given to (i) the development of a stable high-order upwind scheme for the convection term and (ii) the development of a local high-order approximation scheme for the diffusion term. Benchmark problems including the lid-driven triangular-cavity flow are employed to validate the present technique. Accurate results at high values of the Reynolds number are obtained using relatively-coarse grids.

Keywords:

• Cartesian grid
• control volume
• deferred correction technique
• integrated rbf
• upwind scheme

Additional information

Notes on contributors

N Mai-Duy

Nam Mai-Duy is an Associate Professor of Mechanical Engineering at University of Southern Queensland (USQ) and a member of Computational Engineering and Science Research Centre. He received his BE degree in Mechanical Engineering from Ho-Chi-Minh-City University of Technology in 1992 and his PhD degree from USQ in 2002. His main research interests are in the field of Computational Rheology and Mechanics, focussing on the development of meshless and Cartesian-grid RBF-based methods for solving PDEs encountered in fluid mechanics, particulate fluids, and multiscale calculations. He has been awarded several prestigious research fellowships, including University of Sydney Sesquicentennial postdoctoral research fellowship, ARC-APD and ARC-FT.

T Tran-Cong

Thanh Tran-Cong is a Professor of Mechanical Engineering at University of Southern Queensland (USQ) and Executive Director of the Computational Engineering and Science Research Centre (CESRC). He earned his Bachelor of Engineering (Aeronautical) in 1979 and his PhD in Computational Rheology in 1989 from the University of Sydney. He spent five years as a design engineer in private engineering sector between his Bachelor and PhD degrees. His main research interests are in computational rheology and mechanics. His research has been supported by several grants, including ARC-LP and ARC-DP grants.