We present steady solutions of high-speed viscous flows over blunt bodies using a multidomain Chebyshev spectral collocation method. The region within the shock layer is divided into subdomains so that internal layers can be well resolved. In the interiors of the subdomains, the solution is approximated by Chebyshev collocation. At interfaces between subdomains, the advective terms are upwinded and the viscous terms are treated by a penalty method. The method is applied to five flows in the Mach number range 5-25 and Reynolds number range from 2*10~3 to 83*10~4, based on nose radius. Results are compared with experimental data and to a finite difference solution.
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