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Think Before You Compute. A Prelude to Computational Fluid Dynamics. Cambridge Texts in Applied Mathematics

  • ID: 4898249
  • Book
  • May 2020
  • 244 Pages
  • Cambridge University Press
Every fluid dynamicist will at some point need to use computation. Thinking about the physics, constraints and requirements early on will be rewarded with benefits in time, effort, and expense. How these benefits can be realised are illustrated in this guide for would-be researchers and beginning graduate students to some of the standard methods and common pitfalls of computational fluid mechanics. Based on a lecture course the author developed over 20 years, the text is split into three parts. The introduction enables students to solve numerically a basic nonlinear problem by a simple method in just three hours. The follow-up part expands on all the key essentials, including discretisation (finite differences, finite elements and spectral methods), time-stepping, and linear algebra. The final part is a selection of optional advanced topics, including hyperbolic equations, representation of surfaces, boundary integral method, multi-grid method, domain decomposition, fast multipole method, particle methods, and wavelets.
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Part I - A first problem:
1. The driven cavity;
2. Streamfunction-vorticity formulation;
3. Primitive variable formulation;

Part II - Generalities:
4. Finite differences;
5. Finite elements; 6.Spectral methods;
7. Time integration;
8. Linear Algebra;

Part III - Special topics:
9. Software packages and FreeFem++;
10. Hyperbolic equations;
11. Representation of surfaces;
12. Boundary integral method;
13. Fast Poisson solvers;
14. Fast Multipole Method;
15. Nonlinear considerations;
16. Particle methods;
17. Wavelets; Index.
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E. J. Hinch University of Cambridge.

E. J. Hinch has been a teacher and researcher in fluid mechanics and applied mathematics at the University of Cambridge for over 45 years. He is the author of Perturbation Methods (Cambridge University Press, 1991) and has been awarded the Fluid Dynamics prizes of the European Mechanics Society and the American Physical Society Division of Fluid Dynamics.
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