A numerical scheme for unsteady flow of a viscous fluid between elliptic plates

Abstract

A new continuation method has been developed to solve the nonlinear eigenvalue problem describing the unsteady, squeezing flow of a viscous fluid between elliptic plates. Unlike the numerical schemes previously used (e.g. homotopy algorithm), the present scheme is conceptually simple, noniterative, insensitive to the first approximation and works for all values of squeeze number S characterizing the flow. The numerical results compare extremely well with those obtained with sophisticated schemes. Since existing numerical data are limited to three sparsely spaced values of S, additional data are reported for systematically spaced values of squeeze number S and ellipticity parameter [beta]. Although the scheme has been applied to a specific problem, it appears potentially capable of handling a variety of nonlinear eigenvalue problems.