Meshless Algorithm

The gridless methods for two-dimensional steady inviscid flow simulation have been researched in this thesis. A quadrantal point infilling strategy is developed to generate point and combine clouds of points automatically. Based on the explicit time-stepping scheme, Batina's centeral gridless methods have been studied. The implicit time-stepping scheme and AUSM~+-up method have been introduced and extended into gridless method. The comparison between Batina's centeral gridless method and the implicit gridless method with upwind scheme show that the latter has the following advantages: fast speed of convergence, small numerical dissipation, better ability to catch shock, good geometrical flexibility and a wide applied range of Ma number. In order to demonstrate the accuracy and rudeness of the method, NACA0012 airfoil in transonic flow, multi-element airfoil complex flow and a pair of NACA0012 airfoils in supersonic and in hypersonic flow are computed. So this method has great potential on the numerical simulation of complex configurations flow.In this thesis, the Navier-Stokes equations of laminar flow are solved by the gridless method on the base of the flow field is divided into two parts: viscous region and inviscid region. In viscous region, dummy control volume is on the clouds of points and the finite volume algorithm is used just like in grid method. In inviscid region, the inviscid flux can be solved the same way as Euler equations. The viscous flux can be obtained by central difference method. The simulating results of NACA0012 airfoil in sub-critical flow and the Karman vortex street over a circular cylinder can demonstrate the validity of this method.