# Coupled Simulations and Fluid-Structure Interaction

A generic Computational Continuum Mechanics library like OpenFOAM is a natural platform for Fluid-Structure Interaction (FSI): both fluids and structural solvers already exist. Furthermore, doing a simulation in a single software simplifies the operation: there is no need for multi-threaded simulations of software to software coupling. The fact that all OpenFOAM solvers and discretisation methods share the base mesh and matrix support and that various mesh-to-mesh mapping tools are already implemented further simplifies the problem.

Early FSI work in FOAM/OpenFOAM was performed at Imperial College in late 1990-s - but it wasn't easy. With the introduction of multi-zonal support and mesh-based field registration, FSI in the new version is much easier. In this session, we will present the FSI-relevant capabilities and examples of application.

## Background and Tutorials: OpenFOAM Capabilities Supporting FSI

In this session we will review some components relevant for programming FSI in OpenFOAM work and review the new FSI demonstration solver.

• Capability talk by Hrvoje Jasak Capability talk slides
• Multi-Domain Support in the Solver
• Mesh-to-Mesh Coupling Tools: surface and volume interpolation
• Interaction with external software: custom boundary conditions or file-based coupling
• 6-DOF Rigid Motion Solver Development by Dubravko Matijasevic of University of Zagreb , Croatia Abstract Slides

Information on automatic mesh motion will be included in the Engines modelling session

## Examples of FSI Simulations in OpenFOAM

### Self-contained solver for FSI with large structural displacements

• Considering interaction between incompressible Newtonian fluid and St. Venant-Kirchhoff elastic solid
• Fluid flow is modelled using incompressible Navier-Stokes equations in ALE formulation
• Elastic solid deformation is described by the geometrically nonlinear momentum equation in an updated Lagrangian formulation
• Both models are discretised in space using second-order accurate finite volume method
• Temporal discretisation of both models is performed using a fully implicit second-order accurate tree time-levels differencing scheme
• Coupling is performed using loosely-coupled staggered algorithm

Structural solver validation

Temporal and spatial accuracy of the structural dynamic solver is validated before using it in the FSI solver. The picture below shows temporal variation of the beam tip deflection as a result of a suddenly applied traction force at the beam end ($\mathcal{F}$ is dimensionless traction force).

The most deformed shape of the beam is shown in the picture below. The surface of the beam is coloured by the equivalent Cauchy stress.

FSI results

The FSI solver is tested on the flow past a cantilevered elastic square beam. The frequency of the inlet flow velocity pulsation is equal to the first natural frequency of the beam. The picture below shows streamlines pattern and equivalent Cauchy stress at the beam boundary. This calculation is done for the solid-fluid density ratio 100:1. For lower density ratios loosely coupled algorithm becomes unstable.