Steady Shock Tracking, Newton's Method, and the Supersonic
              Blunt Body Problem

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



    The steady shock tracking method, which combines shock tracking and
Newton's method, is applied to the axisymmetric supersonic blunt body
problem. The formulation is in conversation form and uses the constant
total enthalpy condition to reduce the number of unknowns at each finite
difference mesh point. On a transformed computational grid where the bow
shock is a coordinate line, the discrete physical shock locations appear
explicitly as unknowns in a set of finite differnce equations which
couples them to the other unknowns. The space-time characteristic
compatibility conditions for the associated time-dependant problem are
used in formulating the boudnary conditions for the steady problem. The
resulting system is solved using various modifications of Newton's method.
Experiments are repeated with three linear system solvers whose efficiency
is compared. The computed results for flow over a sphere are economically
obtained and agree well with experiment. Continuation of the solutions
with respect to some physical parameters is explored, and multiple solutions
of one variation of finite difference system are displayed.