Abstract: In order to calculate the flutter problems efficiently and accurately, a fully-implicit tightly-coupled algorithm is developed. Subiteration discretizations are constructed respectively for the aerodynamic and structural dynamic equations. By alternately solving the equations with the LU-SGS scheme and the Newmark method in the pseudo time domain, the high-accuracy solutions at each physical time step can be obtained. The aerodynamic equation is solved by the finite volume method on the multiblock structured grid, and the structural calculation adopts the linear model. A grid deformation approach employing the radial basis functions combined with the transfinite interpolation is introduced here to generate a dynamically moving grid. By applying this developed algorithm, the limit cycle oscillation (LCO) of a two-dimensional airfoil model and the linear flutter of AGARD 445.6 wing are simulated. The calculation of a two-dimensional airfoil model obtains the characteristic curves of the LCO amplitude vs non-dimensional freestream velocity, and the flutter boundary of AGARD 445.6 wing exhibits a transonic “pit” distinctly. The calculation results agree well with the literature and experimental value, which implies that this fully-implicit tightly-coupled algorithm can simulate the flutter problems effectively.

Key words: Flutter, Limit cycle oscillation (LCO), Radial basis functions, Tight coupling, Transfinite interpolation, Transonic “pit”