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

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.