This paper describes a Chebyshev collocation method for solving the eigenvalue problem that governs the stability of parallel two-phase flow. The method is based on the expansion of the eigenfunctions in terms of Chebyshev polynomials, point collocation, and the subsequent solution of the resulting generalized eigenvalue problem with the QZ-algorithm. We concentrate on the question how to handle difficulties that arise when these ¿standard¿ techniques are applied to the stability problem of a thin film of liquid that is sheared by a gas. After discussing this specific problem in detail, it is argued that the method of solution can readily be applied to other two-phase flow configurations as well.
Boomkamp, P. A. M., Boersma, B. J., Miesen, R. H. M., & Beijnon, G. V. (1997). A chebyshev collocation method for solving two-phase flow stability problems. Journal of computational physics, 132(2), 191-200. https://doi.org/10.1006/jcph.1996.5571