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.