A monolithical fluid-structure interaction algorithm applied to the piston problem

An investigation of time marching computational fluid-structure interaction algorithms is presented. The analysis is applied to the piston problem. Attention is focussed on the time integration properties of the coupling algorithms. The staggered scheme is first investigated where fluid and structure are alternately integrated by separate solvers in a predictor-corrector fashion. This algorithm suffers from a time lag between the integration of the fluid and structure. The influence of the time lag is investigated by the comparison of different predictions for the structure. A novel monolithical algorithm is then introduced in order to annihilate the time lag. This algorithm integrates fluid, structure and interaction as a single system by an implicit algorithm. Linear acoustic as well as nonlinear Euler equations for gas dynamics are investigated. The numerical results of the staggered scheme reveal a non-physical deviation of the mean position of the piston at higher cn numbers. The deviation of the mean position is not present in the calculation with the monolithical scheme. Stability analysis shows the unconditional stability of the monolithical scheme for the acoustic equations whereas the staggered scheme has a limited domain of stability. This domain can he enlarged by an improvement of the structural prediction. Analysis of the damping shows an energy production in the staggered scheme while the monolithical scheme has no energy production term. The analyses lead to the formulation of the Interaction Consistency Law which prescribes the relation for the time discretisation between fluid and structure solvers and their boundary conditions. (C) 1998 Elsevier Science S.A. All rights reserved.