This chapter introduces fluid–structure interaction (FSI) as a coupled multi-physics problem where fluid flow and structural response influence each other through force, motion, and sometimes thermal exchange. The chapter establishes the conceptual framework of coupled systems, distinguishes between one-way and two-way coupling, and introduces the kinematic descriptions (Lagrangian, Eulerian, ALE) used to formulate FSI problems. The focus is on understanding when coupling matters and how different levels of coupling are classified in engineering simulations.

Context and Motivation

Modern engineering systems rarely involve a single physical field. Structures deform, fluids exert forces, and motion feeds back into the flow.

Typical examples include:

Aeroelasticity of wings and turbine blades
Wind–structure interaction in bridges and skyscrapers
Blood flow in deformable vessels
Sloshing in tanks and pressure surges
Vibrations induced by unsteady flow (VIV, flutter)

In all these cases:

Treating fluid and structure independently can be misleading
The interaction itself may dominate system behavior

FSI provides a framework to capture this interaction consistently.

Coupled Systems: General Concepts

3.1 What Is a Coupled System?

A coupled system consists of:

Multiple subsystems governed by different physical laws
Dynamic interaction through shared interfaces or fields

Key characteristics:

Heterogeneous physics (fluid, solid, thermal, etc.)
Mutual dependency between solution fields
Often nonlinear and multi-scale

3.2 Multi-Field vs Multi-Physics Problems

Multi-field problem
Multiple dependent variables (fields) solved together, possibly within one physics domain
Example: velocity–pressure coupling in incompressible flow
Multi-physics problem
Multiple distinct physical models interacting
Example: fluid flow + structural deformation (FSI)

Important distinction:

Every multi-physics problem is multi-field, but not every multi-field problem is multi-physics.

Fluid–Structure Interaction (FSI)

4.1 Definition

FSI occurs when:

A fluid exerts forces (pressure, shear, thermal loads) on a structure
The structure responds through deformation or motion
This response alters the fluid flow

This creates a feedback loop:

Flow → structural response → modified flow → updated forces

4.2 Physical Interpretation

FSI strength depends on:

Fluid density and velocity
Structural stiffness and mass
Time scales of flow vs structure
Magnitude of deformation

If structural motion significantly changes the flow:

Two-way coupling is required
If not:
One-way coupling may be sufficient

One-Way vs Two-Way Coupling

5.1 One-Way (Weak) Coupling

Process:

Solve fluid problem
Transfer loads to structure
Solve structural response
No feedback to fluid

Valid when:

Structural deformation is small
Flow field is insensitive to deformation
Interest is mainly in stresses or displacements

Typical uses:

Pressure loads on rigid or stiff components
Preliminary structural assessment

5.2 Two-Way (Strong) Coupling

Process:

Fluid and structure exchange data iteratively
Interface conditions are enforced repeatedly

Required when:

Deformations alter flow topology
Added-mass effects are important
Unsteady phenomena dominate (flutter, VIV, sloshing)

Classification of FSI Problems

FSI problems are commonly classified by:

6.1 Physical Coupling Strength

Weak: negligible feedback
Strong: mutual dependency

6.2 Deformation Magnitude

Small deformation (linearized geometry)
Large deformation (mesh motion required)

6.3 Time Dependence

Steady or quasi-steady
Fully transient

6.4 Mesh Compatibility

Conforming interfaces
Non-conforming interfaces with interpolation

Kinematic Descriptions

7.1 Lagrangian Description

Mesh follows material points
Natural for structural mechanics
Difficult for large fluid deformation

Used for:

Solids
Small-deformation fluids

7.2 Eulerian Description

Mesh fixed in space
Fluid flows through control volumes
Natural for CFD

Limitation:

Cannot directly track moving boundaries

7.3 Arbitrary Lagrangian–Eulerian (ALE)

ALE blends both views:

Mesh moves independently of material
Allows boundary motion while controlling mesh distortion

Key role in FSI:

Enables moving fluid–structure interfaces
Foundation of most FSI formulations

Interface Conditions in FSI

At the fluid–structure interface, two conditions must be satisfied:

Kinematic continuity
- Fluid and structure share the same velocity at the interface
Dynamic equilibrium
- Forces transmitted across the interface are equal and opposite

Violating either leads to:

Non-physical results
Numerical instability

Partitioned vs Monolithic Approaches

9.1 Partitioned (Staggered) Approach

Separate solvers for fluid and structure
Data exchanged at interface
Most common in industrial software

Pros:

Flexibility
Reuse of existing solvers

Cons:

Stability issues for strong coupling

9.2 Monolithic Approach

Single system of equations
Strong numerical coupling