Vortex Methods Theory and Practice

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.

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 alternative to finite difference and spectral methods. This book is both a reference monograph and a textbook for computational fluid dynamics courses.