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Full Description
A better understanding of the mechanisms leading a fluid system to exhibit turbulent behavior is one of the grand challenges of the physical and mathematical sciences. Over the last few decades, numerical bifurcation methods have been extended and applied to a number of flow problems to identify critical conditions for fluid instabilities to occur. This book provides a state-of-the-art account of these numerical methods, with much attention to modern linear systems solvers and generalized eigenvalue solvers. These methods also have a broad applicability in industrial, environmental and astrophysical flows. The book is a must-have reference for anyone working in scientific fields where fluid flow instabilities play a role. Exercises at the end of each chapter and Python code for the bifurcation analysis of canonical fluid flow problems provide practice material to get to grips with the methods and concepts presented in the book.
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.
