Numerical analysis of corrugated tube flow using RBFNs

Abstract

[Abstract]: This paper reports the application of neural networks for the numerical analysis of steady-state axisymmetric flow through an indefinitely long corrugated tube. Meshless global radial basis function networks (RBFNs) are employed to represent all dependent variables in the governing differential equations. For a better quality of approximation, the networks used here are constructed based on the integration process rather than the usual differentiation process. Multiple spaces of network weights for each variable are converted into the single space of nodal variable values, resulting in the square system of equations with usual size. The governing equations are discretized in the strong form by point collocation and the resultant nonlinear system is solved with trust-region methods. The corrugated tube flow of a Newtonian fluid, power-law fluid and Oldroyd-B fluid are considered. With relatively low numbers of data points, flow resistance predictions obtained are in good agreement with the benchmark solutions.