# Fluid-structure coupling

As a fluid-structure interaction ( English fluid-structure interaction ) is referred to in engineering considering the mutual influence of the structure and flow. Numerical methods for flow and structure calculation are coupled with one another.

The mutual influence of structure and flow is an interesting phenomenon that occurs frequently in nature and technology. It occurs on elastic, easily deformable, oscillatory, rotatable or displaceable mounted, flowed around or flowed through structures. The separation of eddies can cause the structure around the flow to vibrate noticeably. Flow-induced vibrations occur e.g. B. on airplane wings, on propeller blades, but also in the flow around buildings. If the vibrations are large enough, they in turn influence the flow. Other popular examples of a fluid-structure interaction are the flow in blood vessels or the flow around heart valves.

## Numerical methods

With a numerical simulation, the real behavior of a component or a flow can be reproduced as a model. Common numerical methods for flow and structure calculations are the finite volume method and the finite element method . Both methods are based on the solution of partial differential equations . For this purpose, the calculation area is subdivided into individual cells with the help of a calculation grid (spatial discretization ), in which the differential equations are solved taking into account suitable boundary conditions . The resulting large systems of equations are numerically solved directly or iteratively. The processes under consideration can be stationary (time-independent) or unsteady (time-dependent). In transient processes, the solution is calculated at discrete points in time, the solution at the current time depending on the solutions at earlier points in time (temporal discretization).

## Transfer of boundary conditions

There are basically two solution methods available for solving coupled problems:

### Iterative coupling between fluid and solid

For the fluid-structure coupling, boundary conditions between the programs for flow and structure calculation must be exchanged. The compressive forces and wall shear stresses resulting from the flow act on the adjoining walls and represent a load on the structure. They are interpolated at the boundary surfaces on the structure's calculation grid. The calculation grid on the flow side and on the structure side can be different. If the flow-induced forces lead to a shift or deformation of the structure, the changed position of the computational grid is included as a new boundary condition in the flow simulation in the next calculation step. This process is run through iteratively until the required convergence criterion or the previously determined maximum number of iterations is reached. In the case of transient processes, the solution is then determined at the new point in time.

### Direct solution of the overall system

In addition to the iterative coupling, direct solution methods are used for strong unsteady interactions, whereby a single solution matrix is ​​set up and solved for the entire system (fluid and structure).

## One-sided and two-sided coupling

A real, two-sided fluid-structure coupling exists when the flow is noticeably influenced by the structural change. Often, however, the reaction of the structural change on the flow is so weak that it can be neglected. In this case one speaks of a one-sided fluid-structure coupling.