This chapter addresses the numerical infrastructure required for robust partitioned fluid–structure interaction simulations. It focuses on interface data transfer between non-matching meshes, including mapping, interpolation, and conservation requirements. The chapter also introduces dynamic mesh strategies needed to accommodate structural motion in the fluid domain and concludes with practical stabilization techniques for strongly coupled and unstable FSI cases. Together, these topics define the numerical robustness of industrial FSI simulations.

Why This Chapter Matters

In real industrial FSI problems:

Fluid and structural meshes are never compatible
Solvers are developed independently
Interfaces are geometrically and numerically inconsistent

As a result:

The interface algorithm becomes as important as the solvers themselves
Poor mapping or stabilization can invalidate an otherwise correct model

This chapter explains how those gaps are bridged.

The Fluid–Structure Interface in Partitioned FSI

3.1 Non-Matching Interfaces Are the Norm

Typical reasons for non-matching interfaces:

Different discretization methods (FVM vs FEM)
Different mesh resolutions
Different geometric simplifications
Different departments generating models independently

Thus, interface data transfer is non-trivial by default.

3.2 What Must Be Transferred

Across the interface, FSI requires:

Displacements and velocities (structure → fluid)
Forces, pressures, heat fluxes (fluid → structure)

These must satisfy:

Kinematic continuity
Dynamic equilibrium
Often energy conservation

Data Transfer Pipeline

All partitioned FSI data transfer consists of four conceptual stages:

Pre-processing
Mapping (search)
Interpolation
Post-processing and stabilization

Each stage affects accuracy and stability.

Mapping: Finding Correspondence Between Meshes

5.1 Purpose of Mapping

Mapping answers:

Which target element corresponds to a given source node or face?

This is a geometric search problem, independent of physics.

5.2 Global (Sequential) Mapping

Characteristics:

Each source node searches all target elements
Robust but computationally expensive
Complexity grows quadratically with mesh size

Used mainly for:

Small models
Debugging

5.3 Bucket (Spatial Search) Mapping

Key idea:

Divide space into “buckets”
Restrict search to local regions

Advantages:

Linear scaling
Essential for large industrial models

Trade-off:

Preprocessing overhead

Interpolation: Transferring the Data

6.1 Role of Interpolation

Once correspondence is known, interpolation computes:

Displacement fields on the fluid mesh
Force fields on the structural mesh

Interpolation defines the transformation operators between meshes .

6.2 Common Interpolation Approaches

Nearest-neighbor (robust, low accuracy)
Element-based projection
Weighted residual projection
Spline and radial basis function (RBF) methods

RBF methods:

Handle large deformation well
Preserve smoothness
Higher computational cost

Conservation and Accuracy Requirements

A good FSI interface scheme should:

Preserve rigid-body motion exactly
Conserve forces and energy
Avoid artificial damping or amplification
Maintain smooth force distributions

Violation leads to:

Non-physical energy injection
Shifted stability boundaries
False flutter or damping

External Data Mapping (One-Way Alternative)

Instead of live coupling, loads can be imported via External Data:

Pressure
Temperature
Heat transfer coefficient

Advantages:

Decoupled workflow
Reduced licensing and runtime dependency
Useful for legacy or multi-team workflows

Limitations:

No feedback
No true two-way coupling

Dynamic Mesh: Enabling Moving Boundaries

9.1 Why Dynamic Mesh Is Required

In two-way FSI:

Structural deformation modifies the fluid domain
The CFD mesh must adapt continuously

Dynamic mesh handles this deformation.

9.2 Mesh Smoothing

Mesh topology is preserved; nodes are moved.

Common methods:

Spring smoothing: fast, best for small deformation
Diffusion smoothing: more robust, better quality
Linear elastic solid smoothing: most robust, most expensive

Key idea:

Mesh behaves like a pseudo-solid absorbing boundary motion.

9.3 Remeshing

Used when:

Deformation is large
Cell quality degrades beyond limits

Characteristics:

Cells are deleted and recreated
Solution is interpolated onto new mesh
Higher cost but enables large motion

In practice:

Smoothing + remeshing are often combined.

Dynamic Mesh and System Coupling

Important constraint:

FSI interface faces cannot be remeshed
Remeshing must occur away from the coupling interface

This preserves:

Mapping consistency
Force conservation

Why Stabilization Is Often Necessary

Even with correct physics and mapping:

Strongly coupled FSI can be numerically unstable
Added-mass effects dominate
Oscillations grow within a time step

Typical unstable cases:

Thin structures
Low Young’s modulus
Incompressible fluids

Solution Stabilization in CFD (Fluent)

12.1 Physical Meaning

Stabilization:

Slows down pressure response near moving boundaries
Acts like numerical damping
Does not change the converged solution

It controls how fast equilibrium is approached, not where it is.

12.2 Stabilization Methods

Volume-based stabilization
Coefficient-based stabilization

Key tuning parameter:

Scale factor

Too low:

Instability
Too high:
Over-damped, slow convergence

Practical Stabilization Strategy

Good practice:

Start with no stabilization
Identify oscillations within a time step
Introduce small stabilization
Increase gradually
Monitor force and displacement convergence

Important insight:

Reducing the time step can increase instability in FSI.

Engineering Intuition

Interface algorithms are as critical as solvers
Mapping errors behave like artificial physics
Dynamic mesh quality controls solver stability
Stabilization is not cheating — it is controlled numerical damping
Robust FSI is built bottom-up: mapping → mesh → coupling → stabilization

Study Priorities

If short on time:

Purpose of mapping vs interpolation
Conservation requirements at interfaces
Difference between smoothing and remeshing
Why FSI interfaces cannot be remeshed
Physical meaning of stabilization

Key Takeaways

Partitioned FSI relies on accurate interface data transfer.
Mapping identifies correspondence; interpolation transfers values.
Conservation at the interface is essential for stability.
Dynamic mesh enables structural motion in CFD.
Stabilization controls added-mass-driven instabilities.
Most FSI failures originate at the interface, not in solvers.

Fluid-Structure Interaction Chapter 4: Interpolation and Mapping