We present steady solutions of high speed viscous flows over blunt bodies using a multidomain Chebyshev spectral collocation method. The region with 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, the Mach number range 5-25 and Reynolds number range 2,000 - 83,000, based on nose radius. Results are compared to experimental data and to a finite difference result.
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