THE MESHLESS METHOD FOR UNSTEADY FLOW WITH LARGE-SCALE MOVING BOUNDARY

The meshless method for unsteady flow involving large-scale moving boundaries is studied in this paper. A criterion for whether the point is to be deleted is established, the cloud is rebuilt by a filling method, and the state of the new point is calculated by a linear interpolation method, which serves as the local reestablishment of cloud for dealing with large scale moving points. The algorithm for solving ALE equations based on the meshless method is developed. On the basis of clouds, the spatial derivatives are approximated by using local least-squares curve fitting and the numerical flux is calculated with HLLC scheme, and a multistage Runge-Kutta algorithm is used to advance the equation in time. As an example, a moving piston is simulated, and the numerical results agree well with exact results.  In addition, the flow of airflow passing through a static column and the flow of a column moving in the static flow are simulated and compared with each other, and results indicate  that the method is valid.