Consistency analysis of fluid-structure interaction algorithms

An investigation of time-marching computational fluid-structure interaction algorithms is presented. The analysis is applied to a piston, problem and the attention is focussed on the coupling algorithms. Staggered schemes are first considered. These suffer from a time lag between the integration of the fluid and structure. Then a novel monolithical algorithm is introduced to annihilate the time lag. This algorithm integrates fluid, structure and interaction as a single system of equations. It is also shown that the monolithical algorithm can be simulated by applying several corrector steps on the staggered algorithm. The numerical results of the staggered scheme show a non-physical deviation of the mean position of the piston at higher CFL numbers. This is caused by the violation of the Interaction Consistency Law (ICL). This law is formulated after an energy analysis of the algorithms. The deviation of the mean position is not present in the calculation with the monolithical scheme, since it satisfies the ICL.