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.

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.

Les modeles euleriens sont devenus dans les quinze dernieres annees des outils populaires pour etudier les interactions fluide-structure, car, au contraire des methodes plus classiques de type ALE, ils permettent de resoudre numeriquement ces problemes en se ramenant a une grille et une methode de resolution unique pour les differents milieux. Ce livre s'interesse a cette classe de modeles en adoptant le point de vue original des methodes level-set, utilisees a la fois pour suivre les interfaces fluide-solide, representer les contraintes elastiques des solides et modeliser les forces de contact entre solides. Il combine un eclairage mathematique des modeles, des aspects d'analyse numerique, des codes elementaires et des illustrations numeriques permettant au lecteur de se faire une idee des domaines d'application et des performances de ces modeles. Les pre-requis necessaires pour profiter pleinement de son contenu font partie du bagage scientifique d'eleves de niveau master en mathematiques appliquees ou mecanique theorique. Il sera un outil pedagogique fructueux pour des cours de deuxieme annee de master ou de debut de these, ainsi que pour des chercheurs voulant aborder ou approfondir ce domaine.