Simulation of viscous and viscoelastic flows using a RBF-Galerkin approach

Abstract

In this paper, two-dimensional flows of viscous and viscoelastic fluids are simulated using radial-basis-function networks (RBFNs) and Cartesian grids. To solve the governing equations, high-order approximations based on one-dimensional integrated-RBFNs are employed to approximate the field variables and the Galerkin discretisation formulation is utilised to transform the differential equation into a set of algebraic equations. The main distinguishing feature of the above combination is that two processes, namely the representation of the field variables and the discretisation of the governing equations, are both based on integration. In sharp contrast to conventional Galerkin methods, derivative boundary conditions are presently imposed in an exact manner. Two test problems, namely natural convection of a Newtonian fluid in a concentric annulus and fully-developed flow of an Criminale-Ericksen-Filbey (CEF) fluid in a rectangular duct, are studied. Results obtained are compared with published data in the literature.

Keywords:

• Integrated RBFN
• Galerkin approach
• Cartesian grid
• Newtonian fluid
• viscoelastic fluid

Additional information

Notes on contributors

D Ho-Minh

Dao Ho-Minh received his BE degree in Mechanical Engineering from Ho-Chi-Minh-City University of Technology in 2000 and his PhD degree from University of Southern Queensland (USQ) in 2011. After completion of his PhD degree, he was appointed as a postdoctoral research fellow at Computational Engineering and Science Research Centre, USQ. His current research efforts are focused on computational rheology and RBF-based methods.

N Mai-Duy

Nam Mai-Duy is a 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, focusing on the development of meshless and Cartesian-grid RBF-based methods for solving PDEs encountered in fluid mechanics, particulate fluids and multi-scale 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, and Executive Director of the Computational Engineering and Science Research Centre. 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.