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

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.