A spectral perspective about the accuracy of numerical predictions of flow instabilities

Abstract

The paper discusses the usefulness of information provided by the eigenvalues, eigenfunctions and eigenvectors of flow stability problems, aiming to propose in a spectral perspective an evaluation of the accuracy of the related numerical solution schemes. The presented material further develops the results of past applications of numerical techniques in the analysis of the stability of heated systems containing single-phase, two-phase and supercritical pressure fluids. Since in all these applications both nonlinear and linear stability analyses were performed adopting very similar techniques, information on the different modes of oscillation or excursion exhibited by these systems during unstable behaviour was also made available. These spectral data, whose usefulness was up to now not completely exploited, are now considered in a new perspective, by addressing the simplest of the previously addressed problems both by analytical and numerical means. Information on the level of accuracy obtained by numerical solution techniques in capturing the intrinsic dynamics of the addressed flow systems is presented.