Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows

This paper presents a radial-basis-function (RBF) collocation method for the simulation of two-dimensional fluid-flow problems. To improve the stability of a discrete solution and the quality of derivative approximations, the present RBF networks (RBFNs) are constructed through integration instead of conventional differentiation. Special attention is given to the following two topics: (i) the effective use of integration constants in the solution of the Navier–Stokes equations and (ii) the employment of “local” integrated RBFNs to handle flows with fine structures. Different types of geometries and fluids are considered. The accuracy of the present technique is demonstrated through the solution of several benchmark test problems.