Implicit Calculations of an Aeroelasticity Problem

Abstract

The purpose of this work is to show that a linearized implicit scheme for the flow resolution can be an efficient and accurate method for solving fluid-structure interaction. The fluid is modeled by the Euler equations in two dimensions and the structure by a one (free piston) or a two (NACA0012 airfoil) degrees of freedom system. The schemes are developed using a finite volume/finite element formulation and, stating the moving boundary problem in the space-time domain, the Riemann solver is generalized in a suitable manner. Assuming a modal decomposition for the structure's response, an analytical solution to the equation of motion is obtained. The effects of the linearized implicit scheme on the aeroelastic response are demonstrated on the free piston and the NACA 0012 airfoil problems. In the latter case, we focus on the capability of the linearized implicit scheme to accurately predict the stability limit of the coupled response (wing flutter analysis). Although the above analysis is performed using a rigid transformation, a robust moving mesh strategy is presented for more general 2-D and 3-D deformations.