Spectral Homotopy Analysis Method for PDEs That Model the Unsteady Von Kàrmàn Swirling Flow


School of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa


A spectral homotopy analysis method (SHAM) is used to find numerical solutions for the unsteady viscous flow problem due to an infinite rotating disk. The problem is governed by a set of two fully coupled nonlinear partial differential equations. The method was originally introduced for solutions of nonlinear ordinary differential equations. In this study, its application is extended to a system of nonlinear partial differential equations (PDEs) that model the unsteady von Kàrmàn swirling flow. Numerical values of the pertinent flow properties were generated and validated against results obtained using the Keller-box numerical scheme. The results indicate that the present method is very accurate and can be used as an efficient tool for solving nonlinear PDEs of the type discussed in this paper.