Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian grids

• Published in: Computers & fluids Vol. 44; no. 1; pp. 32 - 42
• Main Authors: Le-Cao, K., Mai-Duy, N., Tran, C.-D., Tran-Cong, T.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.05.2011; Elsevier
• Subjects: Cartesian; Cartesian grid; Computational methods in fluid dynamics; Computer simulation; Convection and heat transfer; Cylinders; Derivatives; Eccentrics; Exact sciences and technology; Fluid dynamics; Fluid flow; Fundamental areas of phenomenology (including applications); Integrated radial-basis-function network; Mathematical analysis; Mathematical models; Multiply-connected domain; Physics; Steady flow; Stream-function formulation; Turbulent flows, convection, and heat transfer; Cartesian grid; Multiply-connected domain; Stream-function formulation; Integrated radial-basis-function network; Eccentricity; Stream function; Annular space; Digital simulation; Natural convection; Two dimensional flow; Radial basis function; Modelling; Coaxial cylinders; Rotating cylinder; Square section; Mesh generation; Heat transfer
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2010.11.027

This paper describes a new numerical procedure, based on point collocation, integrated multiquadric functions and Cartesian grids, for the discretisation of the stream-function formulation for flows of a Newtonian fluid in multiply-connected domains. Three particular issues, namely (i) the derivation of the stream-function values on separate boundaries, (ii) the implementation of cross derivatives in irregular regions, and (iii) the treatment of double boundary conditions, are studied in the context of Cartesian grids and approximants based on integrated multiquadric functions in one dimension. Several test problems, i.e. steady flows between a rotating circular cylinder and a fixed square cylinder and also between eccentric cylinders maintained at different temperatures, are investigated. Results obtained are compared well with numerical data available in the literature.