Author/Authors :
Nowruzi, H Department of Maritime Engineering - Amirkabir University of Technology, Tehran, Iran , Salman Nourazar, S Department of Mechanical Engineering - Amirkabir University of Technology, Tehran, Iran , Ghassemi, H Department of Maritime Engineering - Amirkabir University of Technology, Tehran, Iran
Abstract :
Hydrodynamic stability of Dean flow is studied using two semi-analytical methods of differential transform
method (DTM) and Homotopy perturbation method (HPM). These two methods are evaluated to examine the
effectiveness and accuracy of the solution of considered eigenvalue problem. Very good accordance is
achieved between our semi-analytical results compared to existing numerical data. Based on our analysis, in
the similar number of truncated terms, HPM is more accurate in comparison with DTM. We also concluded
that for the higher wave numbers, HPM provide more accurate results with less truncated terms compared to
the DTM. Finally, we found the critical Dean number 35.927 corresponding to wave number of 3.952 for
onset of instability of Dean flow.
Keywords :
Homotopy perturbation method , Differential transform method , Hydrodynamic stability , Dean flow
