Abstract: The meshless method is used to solve problems with moving boundaries, A method is proposed for dealing with unsteady flow with movable and torsional boundaries in small scale. The moving principle for discrete points in meshless method is formulated, the spring analogy is modified to consider the movements of points, the adaptability and precision of the analogy are enhanced. ALE equations are solved based on meshless method. Based on clouds, the spatial derivatives are approximated by using local least-squares curve fitting and the numerical flux is calculated with HLLC scheme, a multistage Runge-Kutta algorithm is used to advance the equation in time. The oscillating flow of representative airfoils in transonic and supersonic conditions is simulated. The computational results agree well with the experiment data, which indicates that the method is valid.

Key words: meshless method, spring analogy, ALE equations, oscillation, numerical simulation