A contact discontinuity tracking method with a specially designed movi
ng grid is developed to eliminate the interface smearing completely. I
n order to precisely locate the contact surface, an updated Riemann so
lver for unsteady one-dimensional inviscid flows is also developed to
allow consideration of the specific heat ratio change across the shock
wave. These two new computational techniques are illustrated in a hig
h Mach number shock tube flow field computation.