# Radial-basis-function calculations of heat and viscous flows in multiply-connected domains

PhD Thesis

Le-Cao, Khoa. 2011. Radial-basis-function calculations of heat and viscous flows in multiply-connected domains. PhD Thesis Doctor of Philosophy. University of Southern Queensland.
Title Radial-basis-function calculations of heat and viscous flows in multiply-connected domains PhD Thesis Le-Cao, Khoa Mai-Duy, Nam Tran-Cong, Thanh University of Southern Queensland Doctor of Philosophy 233 2011 This PhD research project is concerned with the development of accurate and efficient numerical methods, which are based on one-dimensional integrated radial basis function networks (1D-IRBFNs), point collocation and Cartesian grids,for the numerical simulation of heat and viscous flows in multiply-connected domains, and their applications to the numerical prediction of the material properties of suspensions (i.e. particulate fluids). In the proposed techniques, the employment of 1D-IRBFNs, where the RBFN approximations on each grid line are constructed through integration, provides a powerful means of representing the field variables, while the use of Cartesian grids and point collocation provides an efficient way to discretise the governing equations defined on complicated domains.Firstly, 1D-IRBFN-based methods are developed for the simulation of heat transfer problems governed by Poisson equations in multiply-connected domains. Derivative boundary conditions are imposed in an exact manner withthe help of the integration constants. Secondly, 1D-IRBFN based methods are further developed for the discretisation of the stream-function - vorticity formulation and the stream-function formulation governing the motion of a New-tonian fluid in multiply-connected domains. For the stream-function - vorticity formulation, a novel formula for obtaining a computational vorticity boundary condition on a curved boundary is proposed and successfully verified. Forthe stream-function formulation, double boundary conditions are implemented without the need to use external points or to reduce the number of interior nodes for collocating the governing equations. Processes of implementing crossderivatives and deriving the stream-function values on separate boundaries are presented in detail. Thirdly, for a more efficient discretisation, 1D-IRBFNs are incorporated into the domain embedding technique. The multiply-connecteddomain is transformed into a simply-connected domain, which is more suitable for problems with several unconnected interior moving boundaries. Finally, 1D-IRBFN-based methods are applied to predict the bulk properties of particulatesuspensions under simple shear conditions.All simulated results using Cartesian grids of relatively coarse density agree wellwith other numerical results available in the literature, which indicates that theproposed discretisation schemes are useful numerical techniques for the analysisof heat and viscous flows in multiply-connected domains. radial basis function calculations; heat and viscous flows; multiply-connected domains 490302. Numerical analysis 401204. Computational methods in fluid flow, heat and mass transfer (incl. computational fluid dynamics) 401299. Fluid mechanics and thermal engineering not elsewhere classified 401706. Numerical modelling and mechanical characterisation Computational Engineering and Science Research Centre

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