Shock fitting is presented as a way to compute shocks with spectral methods. With fitting, spectral approximation is performed on smooth portions of the flow and a precise description of a discontinuous shock is possible. Coupled with spectral domain decomposition, one has the ability to resolve efficiently and without stretching transformations, boundary layers and other regions in the flow where increased local resolution is needed. A supersonic blunt body problem is solved to provide an example of the use of the approach. Comparisons between computations and experimental measurements are made for body surface quantities, shock shape, and body normal direction profiles.
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