Steady Shock Tracking and Newton's Method Applied to One-Dimensional
                              Duct Flow



               G.R. Shubin, A.B. Stephens, and H.M. Glaz



     A new computational approach combining shock tracking and Newton's 
method is applied to steady one-dimensional flow through a variable area
duct. On a transformed computational grid where the shock is fixed, the
physical shock location appears explicitly as an unknown in a set of
finite difference equations, and is coupled to the other unknowns. The
space-time characteristics for the associated time-dependent problem are
used in formulating the boundary conditions. The resulting system is solved
by Newton's method. The computed results agree very well with an exact
solution, and the Newton iterates converge rapidly in comparison to some
explicit shock capturing, time-asymptotic methods.