Vortex methods have matured in recent years, offering an interesting alternative to finite difference and spectral methods for high resolution numerical solutions of the Navier Stokes equations. In the past three decades, research into 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, which was the motivation for their introduction. This book presents and analyzes vortex methods as a tool for the direct numerical simulation of impressible viscous flows. It will interest graduate students and researchers in numerical analysis and fluid mechanics and also serve as an ideal textbook for courses in fluid dynamics.
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.
"The authors are to be congratulated on providing the reader with a well-founded, comprehensive introduction to a very attractive and rapidly developing field..." SIAM Review
"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