| Abstract: | A Galerkin finite element method is described for studying the stability of two superposed immiscible Newtonian fluids in plane Poiseuille flow. The formulation results in an algebraic eigenvalue problem of the form Aλ2 + Bλ + C = 0 which, after transforming to a standard generalized eigenvalue problem, is solved by the QR algorithm. The numerical results are in good agreement with previous asymptotic results. Additional results show that the finite element method is ideally suited for studying linear stability of superposed fluids when parameters characterizing the flow fall outside the range amenable to perturbation methods. The applicability of the finite element method to similar eigenvalue problems is demonstrated by analysing the steady-state spatial development of two superposed fluids in a channel. |
