Preface -- Part 1: Novel methods and approaches -- Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow, by L. S. Tuckerman, J. Langham, and A.Willis -- Time-stepping and Krylov methods for large-scale instability problems, by J.-Ch. Loiseau, M. A. Bucci, S. Cherubini, and J.-Ch Robinet -- Spatial and temporal adaptivity in numerical studies of instabilities, with applications to fluid flows, by A.L. Hazel -- Computation of Unstable Periodically Forced Navier-Stokes Solutions-Towards Physical Modal Expansions, by M. Morzynski, B. R. Noack -- On acceleration of Krylov-subspace-based Newton and Arnoldi iterations for incompressible CFD: replacing time steppers and generation of initial guess, by A.Gelfgat -- Part 2: Reviews of methods, approaches, and problems -- Stationary flows and periodic dynamics of binary mixtures in tall laterally heated slots, by J.S.Umbria and M. Net -- A brief history of simple invariant solutions in turbulence, by L.van Veen -- The lid driven cavity, by H. Kuhlmann, and F. Romano -- Instabilities in the wake of an inclined prolate spheroid, by H. I. Andersson, F. Jiang, V. L. Okulov -- Global Galerkin method for stability studies in incompressible CFD and other possible applications, by A. Gelfgat -- Part 3: Some recently solved problems -- Instabilities in extreme magnetoconvection, by O. Zikanov, Y. Listratov, X. Zhang, and V. Sviridov -- A mathematical and numerical framework for the simulation of oscillatory buoyancy and Marangoni convection in rectangular cavities with variable cross section, by M. Lappa -- Continuation for thin film hydrodynamics and related scalar problems, by S. Engelnkemper, S. V. Gurevich, H. Uecker, D. Wetzel, and U. Thiele -- Numerical Bifurcation Analysis of Marine Ice Sheet Models, by T. E. Mulder, H. A. Dijkstra, and F. W. Wubs. .

Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field. .