Spectral methods for the Euler equations. II - Chebyshev methods and shock fitting

The Chebyshev spectral collocation method for the Euler gasdynamic equations is described. It is used with shock fitting to compute several two-dimensional gasdynamic flows. Examples include a shock/acoustic wave interaction, a shock/vortex interaction, and the classical blunt-body problem. With shock fitting, the spectral method has a clear advantage over second-order finite differences in that equivalent accuracy can be obtained with far fewer grid points.