On aerodynamic force computation in fluid–structure interaction problems — Comparison of different approaches

Abstract

This paper is interested in the numerical approximation of a two-dimensional fluid–structure interaction problem. A special attention is paid to the numerical realization of aerodynamic force (AF) calculations. Three different AF computations within finite element method framework are described and compared. First, the extrapolation of fluid stress tensor components from the interior of the fluid domain is the most straightforward method; however, this approach is of lower theoretical accuracy due to the explicit computation of velocity gradient. Second, the local reconstruction method applied on the velocity gradient is based idea of the least square fit of the gradients evaluated at finite element centroids from local patch. Third, the weak reformulation technique using the weak formulation of the fluid flow problem leads to the expression of AF in an integral form. As it avoids direct velocity gradient computation it is of higher accuracy compared to previous methods.The experimental convergence of all mentioned methods for the drag and lift coefficients is tested on the benchmark of a static cylinder in a cross-flow and further extended to the case with prescribed motion of the cylinder. Further, two FSI simulations compare the transferred energy from the fluid to the structure for the case of structure vibrations submerged in the viscous fluid and also for the flow-induced structural vibrations. The critical inlet velocity of flutter instability is determined and it is shown that for a given numerical setting the choice of AF computation can lead to the different FSI behavior.