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About this book

This book is intended to provide a compilation of the state-of-the-art numerical methods for nonlinear fluid-structure interaction using the moving boundary Lagrangian-Eulerian formulation. Single and two-phase viscous incompressible fluid flows are considered with the increasing complexity of structures ranging from rigid-body, linear elastic and nonlinear large deformation to fully-coupled flexible multibody system. This book is unique with regard to computational modeling of such complex fluid-structure interaction problems at high Reynolds numbers, whereby various coupling techniques are introduced and systematically discussed. The techniques are demonstrated for large-scale practical problems in aerospace and marine/offshore engineering.

This book also provides a comprehensive understanding of underlying unsteady physics and coupled mechanical aspects of the fluid-structure interaction from a computational point of view. Using the body-fitted and moving mesh formulations, the physical insights associated with structure-to-fluid mass ratios (i.e., added mass effects), Reynolds number, large structural deformation, free surface, and other interacting physical fields are covered. The book includes the basic tools necessary to build the concepts required for modeling such coupled fluid-structure interaction problems, thus exposing the reader to advanced topics of multiphysics and multiscale phenomena.

Table of Contents

Frontmatter

Chapter 1. Introduction: A Computational Approach

Abstract
This book aims at providing a survey of mathematical formulations and simulation techniques for fluid-structure interactions. As the name suggests, fluid-structure interactions involve the interplay of fluid flow and deformable/moving solid structures, aimed at understanding some physical phenomenon or designing an engineering device.
Rajeev Kumar Jaiman, Vaibhav Joshi

Chapter 2. Equilibrium, Kinematics and Balance Laws

Abstract
When a fluid flows past or inside a structure, loads exerted by the fluid tend to change the configuration of the structure by inducing deformations and/or displacements.
Rajeev Kumar Jaiman, Vaibhav Joshi

Chapter 3. Fluid-Structure Equations with Body-Fitted Interface

Abstract
In this chapter, we combine the balance laws of fluid and solid fields to formulate fluid-structure interactions.
Rajeev Kumar Jaiman, Vaibhav Joshi

Chapter 4. Variational and Stabilized Finite Element Methods

Abstract
Before proceeding with the variational formulation of the fluid-structure coupled system, let us look at the convection-diffusion-reaction (CDR) equation which forms a canonical equation for any continuum transport system. The present chapter discusses the variational formulation and finite element technique applied to the CDR equation and reviews various types of stabilization methods.
Rajeev Kumar Jaiman, Vaibhav Joshi

Chapter 5. Fluid-Structure Interaction: Variational Formulation

Abstract
In the previous chapter, we studied some of the basics of the finite element variational formulation for a transient convection-diffusion-reaction equation, which forms a canonical form for the nonlinear fluid-structure interaction equations.
Rajeev Kumar Jaiman, Vaibhav Joshi

Chapter 6. Quasi-Monolithic Fluid-Structure Formulation

Abstract
In this chapter, we deal with the first type of strategy in solving the fluid-structure interaction system, namely, monolithic techniques.
Rajeev Kumar Jaiman, Vaibhav Joshi

Chapter 7. Partitioned Fluid-Structure Interaction Methods

Abstract
In the previous chapters, we formulated the finite element discretization of the fluid-structure interaction equations and looked into the monolithic type of coupling methods. An essential requirement of such a coupled system is the accurate description of the fluid–structure interface. In the monolithic technique, this feature is naturally taken care by the formulation as the dynamic equilibrium is easily satisfied. In this chapter, we look into the treatment of the fluid-structure interface and interface conditions for partitioned type of methods. While partitioning refers to the decomposition into the fluid and structural subdomains at a given time level, staggering is the sequence in which time integration is carried out along the interface between the subdomains, by satisfying the kinematic and dynamic equilibrium conditions at the interface.
Rajeev Kumar Jaiman, Vaibhav Joshi

Chapter 8. Two-Phase Fluid-Structure Interaction

Abstract
Two-phase fluid-structure interaction is omnipresent. It has applications from offshore pipelines carrying oil or gas [42, 195], marine vessels subjected to free-surface ocean waves, blood flow through arteries and veins, to multiphase flow inside heat exchangers.
Rajeev Kumar Jaiman, Vaibhav Joshi

Chapter 9. Flexible Multibody Fluid-Structure Interaction

Abstract
Interaction between interconnected multiple rigid or flexible bodies with the fluid can be found in engineering applications such as underwater robotics, helicopter rotor dynamics, offshore wind turbines and oil/gas platforms, bio-inspired flying vehicles, among others.
Rajeev Kumar Jaiman, Vaibhav Joshi

Chapter 10. Turbulence Modeling in Fluid-Structure Interaction

Abstract
Continuing the journey of the partitioned-type of coupling techniques, we focus on the modeling of turbulent effects in this chapter. These effects are predominant at high Reynolds numbers and are inherently chaotic and complex to capture by a numerical simulation. The closure problem for the turbulent flow can be broadly solved by three approaches, viz., direct numerical simulation (DNS), unsteady Reynolds averaged Navier-Stokes (RANS), and large eddy simulation (LES). The DNS resolves all the physical turbulent effects and eddies completely, thus it requires the computational mesh refinement to be extremely fine at high Reynolds numbers, leading to a very high computational cost. On the other hand, RANS or unsteady RANS only models the turbulent effects close to the boundary layer, thus being ineffective in capturing separated flow structures in the turbulent wake.
Rajeev Kumar Jaiman, Vaibhav Joshi

Backmatter

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