Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics

1. Front Matter

   Pages i-viii

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2. Novel Methods and Approaches

   1. Front Matter

      Pages 1-1

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   2. Order-of-Magnitude Speedup for Steady States and Traveling Waves via Stokes Preconditioning in Channelflow and Openpipeflow

      • Laurette S. Tuckerman, Jacob Langham, Ashley Willis

      Pages 3-31

   3. Time-Stepping and Krylov Methods for Large-Scale Instability Problems

      • J.-Ch. Loiseau, M. A. Bucci, S. Cherubini, J.-Ch. Robinet

      Pages 33-73

   4. Spatial and Temporal Adaptivity in Numerical Studies of Instabilities, with Applications to Fluid Flows

      • Andrew L. Hazel

      Pages 75-115

   5. Unstable Periodically Forced Navier–Stokes Solutions–Towards Nonlinear First-Principle Reduced-Order Modeling of Actuator Performance

      • Marek Morzyński, Wojciech Szeliga, Bernd R. Noack

      Pages 117-145

   6. On Acceleration of Krylov-Subspace-Based Newton and Arnoldi Iterations for Incompressible CFD: Replacing Time Steppers and Generation of Initial Guess

      • Alexander Gelfgat

      Pages 147-167

3. Reviews of Methods, Approaches, and Problems

   1. Front Matter

      Pages 169-169

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   2. Stationary Flows and Periodic Dynamics of Binary Mixtures in Tall Laterally Heated Slots

      • Juan Sánchez Umbría, Marta Net

      Pages 171-216

   3. A Brief History of Simple Invariant Solutions in Turbulence

      • Lennaert van Veen

      Pages 217-231

   4. The Lid-Driven Cavity

      • Hendrik C. Kuhlmann, Francesco Romanò

      Pages 233-309

   5. Instabilities in the Wake of an Inclined Prolate Spheroid

      • Helge I. Andersson, Fengjian Jiang, Valery L. Okulov

      Pages 311-352

   6. Global Galerkin Method for Stability Studies in Incompressible CFD and Other Possible Applications

      • Alexander Gelfgat

      Pages 353-398

4. Some Recently Solved Problems

   1. Front Matter

      Pages 399-399

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   2. Instabilities in Extreme Magnetoconvection

      • Oleg Zikanov, Yaroslav Listratov, Xuan Zhang, Valentin Sviridov

      Pages 401-417

   3. A Mathematical and Numerical Framework for the Simulation of Oscillatory Buoyancy and Marangoni Convection in Rectangular Cavities with Variable Cross Section

      • Marcello Lappa

      Pages 419-458

   4. Continuation for Thin Film Hydrodynamics and Related Scalar Problems

      • S. Engelnkemper, S. V. Gurevich, H. Uecker, D. Wetzel, U. Thiele

      Pages 459-501

   5. Numerical Bifurcation Analysis of Marine Ice Sheet Models

      • T. E. Mulder, H. A. Dijkstra, F. W. Wubs

      Pages 503-527

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.  

• Computational fluid dynamics
• Bifurcations and stability theory
• Solution branching
• Solution path following
• High performance computing
• 3D fluid dynamics stability
• fluid- and aerodynamics

“The book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures and thereby provides a comprehensive review of recently solved challenging problems in the field.” (Titus Petrila, zbMATH 1398.76005, 2018)

• School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel

  Alexander Gelfgat

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