Application of finite element method in aeroelasticity

• Published in: Journal of computational and applied mathematics Vol. 215; no. 2; pp. 586 - 594
• Main Author: SVACEK, Petr
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.2008; Elsevier
• Subjects: Aeroelasticity; Exact sciences and technology; Finite element method; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Partial differential equations; Sciences and techniques of general use; Finite element method; 76D05; Aeroelasticity; 76M10; 74F10; ALE formulation; Turbulence; Approximation; Lagrangian; Stokes equation; Differential equation; Differential system; Two dimensional flow; Discretization method; Equation system; Incompressible flow; Numerical analysis; Navier Stokes equation; Applied mathematics; Numerical simulation; Two-dimensional calculations; Viscous flow
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2006.04.069

The subject of this paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil, which can rotate around the elastic axis and oscillate in the vertical direction. The numerical simulation consists of the finite element approximation of the Navier–Stokes equations coupled with the system of ordinary differential equations describing the airfoil motion. The arbitrary Lagrangian–Eulerian (ALE) formulation of the Navier–Stokes equations, stabilization the finite element discretization and coupling of both models is discussed. Moreover, the Reynolds averaged Navier–Stokes (RANS) system of equations together with the Spallart–Almaras turbulence model is also discussed. The computational results of aeroelastic calculations are presented and compared with the NASTRAN code solutions.