Numerical boundary condition of Euler equations in cylindrical coordinate

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 center line. 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.