Results are presented for finite element computations involving high speed,
viscous compressible internal and external flows. The stabilized finite-el
ement formulations for the Navier-Stokes equations in the conservation law
form are salved using the conservation variables. To improve the accuracy o
f the base method, especially in the regions of flow that are associated wi
th shocks, boundary-layers and their interactions, the Enhanced-Discretizat
ion Interface-Capturing Technique (EDICT is utilized. An error indicator is
employed to identify the regions in the computational domain that need enh
anced discretization for increased accuracy. The method is implemented on a
shared-memory parallel computer and is used to study complex flows, that i
nvolve shock-wave/boundary-layer interactions, in supersonic diffusers and
wind-tunnels. The start-up problem in supersonic wind-tunnels, caused by a
narrow second throat in the diffuser section, is simulated. This computatio
n brings out some of the very interesting features of the unsteady dynamics
of the start-up shock.