This paper deals with an adaptive dynamic grid around oscillationg airfoils and compares Roe upwind methods, with scalar and CUSP central difference schemes. Euler equations have been solved for the external invisid compressible flow. Thus, at first, the equations were written into the integrated form, and then in CUSP and Scalar schemes, by means of the central difference method, and in Roe scheme, by means of the upwind difference method, they were made into the discritized form. In this paper, these schemes will be introduced, and the results of these methods will be compared. To adapt grids, when bodies move or rotate, the spring network analisys is used. In this paper edges are replaced with linear springs. Some numerical solutions are run to balance forces, applies to springs that connected to a node, by displacements. a logical definition is assumed for linear spring coefficient and displacement of nodes. All we have done, are for structured meshes for airfoil. Then boundaries are moved or rotated and meshes are refined by using spring network analogy.

Keywords