Solution Of Euler/N-S Equations Using Gridless Methods

An explicit gridless method for solving Euler/Navier-Stokes equations is presented in this paper. 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 discrete form for Euler equations on base of gridless method , and adopts five steps Runge-Kutta scheme for time-marching. The numerical results have been obtained for the 2-D flows over airfoils or multi-element airfoils using the method presented. The preliminary results obtained by solving N-S equations show- viscous effects clearly. In addition, based on Euler equations the effects of point distribution, cloud structure and weight selection on computational results have been analyzed, which results in having a convenient technique of point distribution in the computational domain and a rule of point selection forming an appropriate. clouds of points used in the computation.