This monograph is devoted to Eulerian models for fluid-structure interaction by applying the original point of view of level set methods.

In the last 15 years, Eulerian models have become popular tools for studying fluid-structure interaction problems. One major advantage compared to more conventional methods such as ALE methods is that they allow the use of a single grid and a single discretization method for the different media. Level set methods in addition provide a general framework to follow the fluid-solid interfaces, to represent the elastic stresses of solids, and to model the contact forces between solids.

This book offers a combination of mathematical modeling, aspects of numerical analysis, elementary codes and numerical illustrations, providing the reader with insights into the applications and performance of these models.

Assuming background at the level of a Masters degree, Level Set Methods for Fluid-Structure Interaction provides researchers in the fields of numerical analysis of PDEs, theoretical and computational mechanics with a basic reference on the topic. Its pedagogical style and organization make it particularly suitable for graduate students and young researchers.

Georges-Henri Cottet is Professor Emeritus at the University of Grenoble-Alpes and honorary member of the Institut Universitaire de France. A specialist in the numerical analysis of partial differential equations, he is interested in numerical methods applied to fluid mechanics, fluid-structure interaction problems and image processing.Emmanuel Maitre is Professor at Grenoble INP-UGA. His research focuses on the analysis and numerical simulation of partial differential equations, interface capture methods and numerical optimal transport, with applications in biomechanics and image analysis.Thomas Milcent is Assistant Professor at Arts et Métiers Bordeaux. His research focuses on numerical methods for fluid-structure interaction and interface transport.

1. Level Set methods and Lagrangian interfaces.- 2. Mathematical tools for continuum mechanics.- 3. Interaction of an incompressible fluid with an elastic membrane.- 4. Immersed bodies : the case of elastic bodies.- 5. Immersed bodies : the case of rigid bodies.- 6. Interaction between bodies by the Level Set method.- 7. Appendix.- 8. References.