I am trying to simulate the steady, two-dimensional compressible flow in a converging-diverging nozzle. In particular, the flow in the diverging section has a normal shock wave somewhere. The location of the shock is unknown, it is determined in the solution where the pressure abruptly increases. The unknowns of the problem are: pressure (P), temperature (T), density (rho), velocity field (radial component: V_r, and axial component: V_z). The governing equations are: conservation of mass, momentum, energy and equation of state. Even though the equation set is hyperbolic by nature, the problem should be elliptic because information travels from both boundaries (inlet and outlet).