Abstract: A method for the treatment of polar singularities of Euler equations is given. The first radial mesh point locates at a half-space away from the centerline. Based on the characteristics of the physical variables,the boundary near centerline is extended so that a high order finite difference scheme can be utilized as at inner mesh points.Similarly,in azimuthal direction the boundary is extended according to the periodicity.An uniform high-order precision is preserved during discretization of equations.

Key words: cylindrical coordinates, polar singularities, high-order finite difference schemes