Think Before You Compute: A Prelude to Computational Fluid Dynamics: 61 (Cambridge Texts in Applied Mathematics, Series Number 61)
Cambridge University Press, 4/30/2020
EAN 9781108479547, ISBN10: 1108479545
Hardcover, 242 pages, 22.9 x 15.2 x 1.7 cm
Language: English
Originally published in English
Every fluid dynamicist will at some point need to use computation. Thinking about the physics, constraints and the requirements early on will be rewarded with benefits in time, effort, accuracy and expense. How these benefits can be realised is 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 that the author has developed over twenty years, the text is split into three parts. The quick 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, the representation of surfaces, the boundary integral method, the multigrid method, domain decomposition, the fast multipole method, particle methods and wavelets.
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.