Gridless Method For The Simulation Of Transonic And Supersonic Flows

The main purpose of this thesis is to develop a gridless method of the solutionof the Euler equations, and its application in the simulation of transonic andsupersonic flows. The following results are obtained in this thesis:(1) On the discretization of computational region, a method for generatingpoints based on Advancing Front Technique is developed. When programming, anew data structure—bidirectional annular adjacency list which reduces thetime and improves the discretization efficient is applied. Then, the operations assearching, deleting and inserting become more effective.(2) Clouds with points are built on the base of a number of discrete grid nodes.In each cloud, local least-squares curve fits are applied to obtain the spatialderivatives. And HLLC's approximate Riemann solver is used for the estimation ofthe numerical flux. In order to improve the accuracy of the shock wave computation,a method of flux limitation is employed. At the same time, an explicit multistageRunge-Kutta algorithm is used to advance the flow equations in time.(3) In order to demonstrate the accuracy and applicability of the gridlessmethod discussed in this thesis, Riemann problem and Emery problem etc arecomputed respectively, and the results are satisfying. Then, the method is used tosimulate high-speed projectile flow, and the results agree well with the laboratorialphotos. With that, the NACA0012 airfoil in transonic flow, two parallel NACA0012airfoils in transonic and in supersonic flow are computed. According to the results, itproves again the accuracy, applicability and ability of catching sharp waves of thisgridless method.