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The goal of this book is to present and analyse vortex methods as a tool for the direct numerical simulation of incompressible viscous flows.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 two decades research in the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the convergence features of the method and several new tools have been developed to generalise its application. 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.