Integrated radial basis function methods for Newtonian and non-Newtonian fluid flows

PhD Thesis


Ho-Minh, Dao. 2011. Integrated radial basis function methods for Newtonian and non-Newtonian fluid flows. PhD Thesis Doctor of Philosophy. University of Southern Queensland.
Title

Integrated radial basis function methods for Newtonian and non-Newtonian fluid flows

TypePhD Thesis
Authors
AuthorHo-Minh, Dao
SupervisorMai-Duy, Nam
Tran-Cong, Thanh
Institution of OriginUniversity of Southern Queensland
Qualification NameDoctor of Philosophy
Number of Pages185
Year2011
Abstract

In this PhD thesis, one-dimensional integrated radial basis function networks (1D-IRBFNs) are further developed for the simulation of viscous and viscoelastic flows in two dimensions. The thesis consists of two main parts.

In the first part, 1D-IRBFNs are incorporated into the Galerkin formulation to simulate viscous flows. The governing equations are taken in the streamfunction-
vorticity formulation and in the streamfunction formulation. Boundary conditions are effectively imposed with the help of the integration constants. The
proposed 1D-IRBFN-based Galerkin methods are validated through the numerical simulation of several benchmark test problems including free convection in a square slot and in a concentric annulus.

In the second part, 1D-IRBFNs are incorporated into the Galerkin and collocation formulations to simulate viscoelastic flows. The momentum and continuity
equations are taken in the streamfunction-vorticity formulation and two types of fluid, namely Oldroyd-B and CEF models, are considered. Flows in a rectangular duct and in straight and corrugated tubes are simulated to validate the proposed 1D-IRBFN-based Galerkin/Collocation methods.

Main attractive features of the proposed methods include (i) easy implementation; (ii) avoidance of the reduction in convergence rate caused by differentiation; and (iii) effective treatment of derivative boundary conditions. Numerical results show that the proposed methods are stable, high-order accurate and converge well. This study further demonstrates the great potential of using
RBFs in CFD.

Keywordsradial basis function networks; Newtonian fluid flows; non-Newtonian fluid flows
ANZSRC Field of Research 2020401706. Numerical modelling and mechanical characterisation
Byline AffiliationsComputational Engineering and Science Research Centre
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