Two Semi-Analytical Methods Applied to Hydrodynamic Stability of Dean Flow

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

• Hydrodynamic stability; Dean flow; Differential transform method; Homotopy perturbation method.