A study of meshless and finite element approaches for aeroelastic analysis on interacting surfaces.

摘要

The ability to handle relative motion of intersecting surfaces remains a difficult yet important problem in the field of computational aeroelasticity. An example of this is simulating the flow over an airfoil with a moving flap or aileron. Traditionally, mesh based methods have handled such problems by solving and re-meshing the domain reiteratively. Although a considerable amount of success has been achieved using these methods, implementing them for problems with a very large number of degrees of freedom is an expensive task even today.;This work focuses on this problem with the objective of developing a numerical framework that will provide an alternative to re-meshing, and mitigate numerical costs traditionally involved in aeroelastic type of problems. To this end a meshless method is first utilized and adapted for unsteady analysis using fluid Euler equations. Bearing in mind certain advantages of the method, and in light of several shortcomings, a finite element approach is next adopted. The premise of the FEM-based method is contingent on decomposing the computational domain based on certain geometric considerations. The solution method involves creating an interpolation space and blending the finite element solution in a zone of transition by using certain mesh-specific 'influence coefficients'. Several implementation issues, such as the construction of the influence coefficients, the creation of a transition zone, imposition of essential boundary conditions, mesh motion, and time integration are addressed and discussed. The method is validated on an airfoil-flap system, with unsteady results for airfoil-pitching and harmonic flap-oscillations compared to those from Theodorsen's thin airfoil theory.