A Study And Application Of Gridless Method For Euler Equations

The basic theory of gridless method and its applications for Computational Fluid Dynamics are investigated in this dissertation. Only clouds of points instead of grids are distributed over the computational domain and the spatial derivatives are estimated using a least-square curve fit on local clouds of points. The paper gives three familiar discrete forms of the spatial derivatives, and adopts explicit five-steps Runge-Kutta scheme for time-marching to solve the discrete form for Euler equations firstly. The numerical results have been obtained for the Riemann question, the flows over the cylinder, and one or two staggered airfoils. The subsequent numerical implementations of the implicit gridless method are presented for the flows over RAE2822 and two staggered airfoils by using LU-SGS algorithm. At last the adaptive method of gridless method is also tested preliminarily and has definite effects.