Variable Mesh Numerical Method for Solving the Orr-Sommerfeld Equation

Abstract

A numerical method using a nonuniform mesh spacing has been developed for solving the Orr-Sommerfield equation and has been used to explore a puzzling detail in the curve of neutral stability at large values of the Reynolds number. The numerical method consists of the usual finite-difference method, an automatically determined variable mesh, and a modified eigenvalue-search-procedure. For plane Poiseuille flow it is demonstrated that the kink in the curve of neutral stability is a feature of solutions of the Orr-Sommerfeld equation and not just a deficiency in the asymptotic analysis as previously suggested.