Vortex Methods
Theory and Practice

This book presents and analyses vortex methods as a tool for the direct numerical simulation of incompressible viscous flows.

Georges-Henri Cottet (Author), Petros D. Koumoutsakos (Author)

9780521621861, Cambridge University Press

Hardback, published 13 March 2000

328 pages, 60 b/w illus.
23.4 x 15.6 x 1.9 cm, 0.64 kg

"Overall, this book gives an excellent review of the analysis and the performance of many state-of-the-art methods in the literature." Mathematical Reviews

This book presents and analyses vortex methods as a tool for the direct numerical simulation of incompressible viscous flows. Vortex methods have matured, offering an interesting alternative to finite difference and spectral methods for high-resolution numerical solutions of the Navier–Stokes equations. Research in the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character that was the motivation for their introduction. Scientists working in the areas of numerical analysis and fluid mechanics will benefit from this book, which may serve both communities as both a reference monograph and a textbook for computational fluid dynamics courses.

1. Definitions and governing equations
2. Vortex methods for incompressible two-dimensional flows
3. Three-dimensional vortex methods for inviscid flows
4. Inviscid boundary conditions
5. Viscous vortex methods
6. Vorticity boundary conditions for the Navier–Stokes equations
7. Lagrangian grid distortions: problems and solutions
8. Hybrid methods
Appendix A. Mathematical tools for the numerical analysis of vortex methods
Appendix B. Fast multipole methods for three-dimensional N-body problems.

Subject Areas: Maths for engineers [TBJ]