Premium
Analysis of superposed fluids by the finite element method: Linear stability and flow development
Author(s) -
Yiantsios Stergios,
Higgins Brian G.
Publication year - 1987
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650070305
Subject(s) - hagen–poiseuille equation , finite element method , eigenvalues and eigenvectors , galerkin method , mathematics , newtonian fluid , mixed finite element method , linear stability , mathematical analysis , flow (mathematics) , geometry , mechanics , physics , instability , quantum mechanics , thermodynamics
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 Aλ 2 + 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.