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.
Sunica ani is a Professor at the University of California, Berkeley, USA. She holds a PhD in Applied Mathematics (1992) from the State University of New York, Stony Brook, and a Masters Degree in Applied Mathematics (1986) from the University of Zagreb, Croatia.
Jeffrey Kuan is a Postdoctoral Research Fellow at the University of Maryland, College Park, USA. He completed his PhD studies in Mathematics (2023) at the University of California, Berkeley, USA.
Boris Muha is a Professor at the University of Zagreb, Croatia. He holds a PhD in Mathematics (2010) from the University of Zagreb, Croatia.
Krutika Tawri is a Visiting Assistant Professor at the University of California at Berkeley, USA. She holds a PhD in Mathematics (2022) from Indiana University in Bloomington, USA.
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