Analysis of viscoelastic flow by a radial basis function networks method

Abstract

[Abstract]: This paper presents a new mesh-free numerical method based on MultiQuadric (MQ) Radial Basis Function Networks (RBFNs) for the analysis of viscoelastic flows. The method uses universal approximation RBFNs to represent the numerical solution of Partial Differential Equations (PDEs) governing viscoelastic flows. The main advantages of the method are its mesh-free nature and ease of implementation. The working of the method is demonstrated in detail with the simulation of the viscoelastic flow through straight (Poiseuille flow) and corrugated tubes. In the case of corrugated tube flow, the irregularly shaped domain is extended to a regularly shaped one in order to simplify the pre-processing. The method achieves the Weissenberg number of at least up to 100 for the Poiseuille flow of UCM and Oldroyd-B fluids using a collocation density of 6 x 6 and about 4 for the corrugated tube flow of Oldroyd-B fluid using a collocation density of 13 X 25.