## Preprint 2010-05

## Maria G. Armentano, Claudio Padra, Rodolfo Rodríguez, Mario Scheble:

### An hp finite element adaptive method to compute the vibration modes of a fluid-solid coupled system

### Abstract:

In this paper we propose an hp-finite element method to solve a two-dimensional fluid-structure vibration problem. This problem arises from the computation of the vibration modes of a bundle of parallel tubes immersed in an incompressible fluid. We use a residual-type a posteriori error indicator to guide an hp-adaptive algorithm. Since the tubes are allowed to be different, the weak formulation is a non-standard generalized eigenvalue problem. This feature is inherited by the algebraic system obtained by the discretization process. We introduce an algebraic technique to solve this particular spectral problem. We report several numerical tests which allow us to assess the performance of the scheme.

This preprint gave rise to the following definitive publication(s):

**Maria G. ARMENTANO, Claudio PADRA, Rodolfo RODRíGUEZ, Mario SCHEBLE: ***An hp finite element adaptive method to compute the vibration modes of a fluid-solid coupled system*. Computer Modeling in Engineering & Sciences, vol. 84, 4, pp. 359-382, (2012).