This article reviews linear instability analysis of flows over or through complex two-
dimensional (2D) and 3D geometries. In the three decades since it first appeared in the …

Asynchronous iterations arise naturally on parallel computers if one wants to minimize idle
times. This paper reviews certain models of asynchronous iterations, using a common …

This book describes numerical methods for the detection, computation, and continuation
(following paths) of equilibria and bifurcation points of equilibria of dynamical systems. In the …

IT is well known that laminar Ŋ ows in two-dimensional channels with discontinuous,
symmetric expansions can produce either symmetric or nonsymmetric solutions, depending …

This paper is concerned with the precise localization of Hopf bifurcations in various fluid flow
problems. This is when a stationary solution loses stability and often becomes periodic in …

In this review we discuss bifurcation theory in a Banach space setting using the singularity
theory developed by Golubitsky and Schaeffer to classify bifurcation points. The numerical …

The article describes a complete numerical solution of a recently formulated benchmark
problem devoted to the parametric study of Rayleigh–Bénard instability in rectangular two …

The eigensolution method, more flexible and efficient than previously used for global non-
parallel flow stability analysis, is presented. The differential eigenvalue problem, resulting …

Free convection in liquid metals is of significant practical interest to the crystal-growing
community since the adverse effects of convective instabilities in the melt phase can be …

Hydrodynamic linear stability analysis of large-scale three-dimensional configurations is
usually performed with a “time-stepping” approach, based on the adaptation of existing …