The Research On Gridless Method For Complex Unsteady Flows Involving Moving Boundaries

Parallel gridless method based on dynamic clouds of points was developed to solve unsteady flows involving moving bodies.Spring analogy and local cloud rebuilding technology was respectively applied to deal with small and large deforming clouds of points. The spring analogy was modified to control the movements of points, the adaptation of the analogy was enhanced, and the results indicated that the spring analogy was more suitable for unsteady flows involving torsion body. The standard for whether the point should be deleted was established, the clouds of points was rebuilded by filling method, the state of the new point is calculated by linear interpolation method, so the local reestablishment of clouds of points for dealing with large scale moving points was accomplished. Besides, points on some boundaries may slip in the tangent direction which resulted in invalid clouds of points. To resolve this problem, these boundaries were defined as deformable boundaries where the points and its clouds can adaptively adjust their positions. The method for dynamic clouds of points used to deal with the deforming clouds of points caused by the moving bodies was proved to be effective.The algorithm for solving Arbitrary Lagrangian-Eulerian(ALE) formulation based on gridless method is accomplished. On the base of clouds in the computational region, the spatial derivatives are approximated by local least-square curve fits, HLLC(Harten, Lax, van Leer, Contact) scheme is extended into the gridless method to calculate the numerical flux and a method of flux limiter is employed in order to improve the accuracy, a multistage Runge-Kutta algorithm is used to advance the equation in time. The numerical results indicated that the method is successful and good at catching shock waves.Delaunay triangulation was used to form the random distributed discrete points into triangular mesh. The geometry and the flow information of points, the triangle and the boundary information were outputted into after-treatment software for the visualization of the gridless results. The display of the results indicated that the method for visualization was useful.Parallel arithmetic based on PC, local network and SPMD module was discussed. The computational area was divided into some small areas, the communication between different computers was completed by MPI messages. The calculation speed was efficiency accelerated and the scale of the computational problems was extended, and the effect was more obvious when solving3D problems. Based on the methods discussed above, Riemann problem and Emery problem were computed to demonstrate the accuracy of the gridless method using HLLC scheme. The oscillatory pitching movement and the plunging movement of representative airfoils, the piston problem were simulated which indicated that the method was successful for dealing with the unsteady flows involving moving bodies whose motion pattern were known. The multi-body interference flow and the muzzle flow field were simulated which indicated that the gridless method coupled with the movement of rigid body was feasible. The method for solving ALE formulation based on dynamic clouds of points gridless method was successful.