2. Basic Governing Equations

In this paper fluid-structure interaction problems are studied from the point of view of aeroelasticity.

The fluid movement exerts aerodynamic forces on the structure which reacts and in turn forces the flow to evolve at the interface with an interface velocity represented by . This produces the coupling effect. The boundary is time dependent, which means that within the Eulerian frame of reference of the fluid, the domain in which the fluid evolves deforms in time. The consequent discretisation of the governing equations for the fluid takes into account this effect, as does also the spatial discretisation (the computational fluid mesh which now is a moving and deforming mesh). The fluid equations for a moving domain are given here using the Arbitrary Lagrange Euler formulation, [DON 82]. There are several techniques to describe the deforming mesh, here two different techniques are used. The first treats the mesh as an elastic system, the mesh segments being replaced by springs of various complexity, the second method exploits the fact that the geometries are identical airfoils or blades, and using mesh re-generation with transfinite interpolation and elliptic smoothing. It has been shown in [BLO 98a], [CAR 88], [GR 96] that these are in fact identical methods when linear elastic springs are used in the mesh deformation formulation.

The so-called coupled trio fluid-structure-mesh hence forms a coupled mechanical system. The coupling in the time domain is obtained by solving simultaneously the systems of the structural and the fluid equations.

The...