Deterministic and Stochastic Fluid-Structure Interaction

This book explores the most recent developments in the field of deterministic and stochastic fluid-structure interaction (FSI), which describes the coupled dynamical interaction between fluids and deformable structures. These sorts of problems arise in many real-life applications, including modeling blood flow in the human cardiovascular system, modeling bioartificial organs, and modeling large-scale structures such as wings, bridges, and dams.

This work primarily focuses on the mathematical well-posedness of fluid-structure interaction (FSI) problems. It introduces a constructive theory in which solutions are built through a time-discretization approach based on operator-splitting strategies. This method has proven to be robust in analyzing FSI problems within both deterministic and probabilistic frameworks and can serve as a foundational framework for developing numerical schemes to effectively compute solutions to these highly complex multiphysics problems.

As FSI is prevalent in science, a rigorous analysis of such coupled fluid-structure systems is key for continued technological development and progress in engineering. Consequently, this book can potentially benefit a broad range of readers, from advanced undergraduate and graduate students to researchers with a background in partial differential equations and fluid dynamics.

Introduction and Outline. - Part I. Preliminaries. - Deterministic preliminaries. - Probabilistic preliminaries. - Part II. Deterministic fluid-structure interaction. - Deterministic FSI with linear coupling. - Deterministic FSI with nonlinear coupling. - Extensions of the splitting scheme. - Part III. Stochastic fluid-structure interaction (SFSI). - Stochastic FSI - A reduced model. - Stochastic FSI - A fully coupled model with linear coupling. - Stochastic FSI - A fully coupled model with nonlinear coupling. - Part IV: Deterministic fluid-poroelastic structure interaction (FPSI). - FPSI with linear coupling. - FPSI with nonlinear coupling. - Bibliography. - Index.