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

MARÍA GABRIELA ARMENTANO, CLAUDIO PADRA, RODOLFO RODRIGUEZ, MARIO SCHEBLE

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES

TECH SCIENCE PRESS

Lugar: Forsyth, GA, USA; Año: 2012 vol. 84 p. 359 - 382

1526-1492

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 ormulation 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.