Table of Contents

1. Transitions in Fluid Flows; 2. Dynamical systems background; 3. Well-posed problems; 4. Discretization of PDEs; 5. Numerical bifurcation analysis; 6. Matrix-based techniques; 7. Stationary iterative methods; 8. Non-stationary iterative methods; 9. Matrix free techniques; 10; Benchmark results for canonical problems; Appendix A: Proofs related to Chapter 3; Appendix B: Relevant Linear Algebra; Appendix C: Proof of inf-sup condition for Stokes; References; Index.

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A guide to computing bifurcation diagrams for fluid flows, including relevant code, with broad applicability to industrial, environmental, astrophysical flows.

About the Author

Henk A. Dijkstra is professor of dynamical oceanography at the Institute for Marine and Atmospheric Research Utrecht (IMAU) within the Department of Physics and Astronomy at Utrecht University, The Netherlands. Henk A. Dijkstra is professor of dynamical oceanography at the Institute for Marine and Atmospheric Research Utrecht (IMAU) within the Department of Physics and Astronomy at Utrecht University, The Netherlands. He has been a member of the Dutch Royal Academy of Arts and Sciences (KNAW) since 2002. He received the Lewis Fry Richardson medal from the European Geosciences Union in 2005, he was elected a Fellow of the Society for Industrial and Applied Mathematics (SIAM) in 2009, and he was awarded an Advanced Grant from the European Research Council in 2021. He is author of several books, including Nonlinear Physical Oceanography (Springer, 2005), Dynamical Oceanography (2008), Nonlinear Climate Dynamics (Cambridge University Press, 2013) and Networks in Climate (Cambridge University Press, 2019). Fred W. Wubs is associate professor of numerical mathematics at the Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence within the Faculty of Science and Engineering of the University of Groningen, The Netherlands. He is the (co-)author of almost seventy publications in the areas of numerical treatment of (stochastic) partial differential equations, preconditioning of sparse linear systems, solution of large sparse eigenvalue problems and high-performance computing.