Symmetric and Non-Symmetric Formulations for Fluid-Structure Interaction Problems: Reference Test Cases for Numerical Developments in a Commercial Finite Element Code

The present paper deals with numerical analysis of fluid-structure interaction problems with commercial finite element codes. The various fluid-structure formulations are today well known from a theoretical point of view, but their application to the dynamic analysis of industrial problems with spectral methods can not be performed with all available codes. The present study exposes a developing process currently undertaken in order to integrate symmetric FSI formulation within the commercial finite element code Ansys. This process is carried out in several steps which are detailed here: first, on overview of the existing fluid-structure formulations is exposed with the view to comparing various finite element codes. Then, coupled symmetric and non-symmetric formulations are recalled on two general FSI problems (elasto-acoustic and hydro-elastic problems) and applied on a generic reference test case. Numerical integration of the presented methods is performed on the Ansys code in the following direction: free surface condition for sloshing mode in pressure formulation, harmonic axi-symmetric pressure fluid formulation for coupled axi-symmetric calculations, general symmetric coupled formulation in u,p,φ (for elasto-acoustic problems with fluid free surface without sloshing) and u,p,η (hydro-elastic problems with fluid free surface with sloshing) formulations. Elementary validations of the implemented methods are proposed by comparing Ansys numerical results to calculations results obtained with a finite element code developed by DCN Propulsion, and presented in the paper. All the developments will be available in future release of the Ansys code in the coming years for the benefit of the Ansys users’ community.