5. Method “COUPLAGE”#

This method is dedicated to fluid-structure coupling with*Code_Saturne* for the fluid domain. It is based on the “COLLOCATION” method taking into account the specificities of the fluid-structure problems envisaged (cf. [bib2]).

We therefore seek to project data from a fluid mesh onto a structural mesh, and vice versa.

The structural mesh is based on an EF discretization, therefore with the knowledge of associated shape functions, while the fluid mesh is based on a discretization in finite volumes (VF), therefore without shape functions a priori. The kinematic fields on the VF fluid domain are defined at the vertex nodes while their dual fields (forces) are constant per face and defined in the middle of the faces.

In addition, the structural mesh is very generally much coarser than the fluid mesh (which must be very refined at the wall in order to properly represent the boundary layer).

The first step of pairing the nodes of the fluid mesh on the solid is done by a conventional “COLLOCATION” method. Note that this method can only be used to generate the mesh correspondence matrix data structure (CORRESP_2_MAILLA cf. documentation U4.72.05). This data structure will then be reused by the exchange operators at the interfaces for fluid-structure coupling:

ENV_CINE_YACS (to send the displacement fields and speed to the fluid code,*cf. documentation U7.06.11),

MODI_CHAR_YACS (to recover fluid forces and add them to the existing structure load,*cf. documentation U7.06.22).

Apart from this limitation, the main difference with the “COLLOCATION” method will be in the construction of the correspondence matrix data structure (CORRESP_2_MAILLA confer documentation U4.72.05) as output from PROJ_CHAMP.

In fact, we will try to best respect the conservation of energy at the interface, and therefore the conservation of the work of discretized efforts during the transition from fluid to solid (cf. [bib2]). Of course, this result is only valid under specific hypotheses:

  • constant fluid force fields per element,

  • finer fluid mesh than solid mesh,

matching method of type “COLLOCATION” from*Code_Aster.

In practice, for any fluid-structure problem, we will have to use the “COUPLAGE” method twice in order to calculate two mesh correspondence data structures. In fact, it is necessary to manage separately the projection of kinematic fields, which is based on fluid fields defined at the top nodes of the fluid mesh, from that of the forces that are defined in the middle of the fluid faces. In each of these two cases, the corresponding fluid mesh will be either the mesh of the vertex nodes or that of the middle nodes of the faces. The projection method is then the same and the structural mesh is unique. All fluid fields (movements, speeds and interface forces) will be considered by*Code_Aster* as fields with classic nodes.