AIAA-2004-0655 Verification and Validation of Pseudospectral Shock Fitted Simulations of Supersonic Flow over a Blunt Body

A highly accurate pseudospectral solver for the inviscid, supersonic flow of a calorically perfect ideal gas over arbitrary axisymmetric blunt body geometries is verified in its ability to approximate solutions to the Euler equations to within a dimensionless error tolerance of 10 in predictions of flow quantities and validated to within a dimensionless error tolerance of 10 in comparison of its predictions of shock location with experimental observation. In space, an exponential grid convergence rate in the L∞[Ω] error in density is predicted due to fitting of the detached bow shock and approximation of spatial derivatives via basis functions with global support; in contrast, a more standard shock capturing scheme will necessarily converge at only first order due to the corrupting influences of large numerical viscosity in the vicinity of the shock, rendering verification and validation more difficult. In time, casting the discrete form of the governing equations in the standard form dx dt = q(x) allows the use of a standard algorithm which enables high accuracy in time integration as well. Verification is accomplished by comparison with known exact solutions in appropriate limits, computation of the alignment of velocity vectors with entropy gradient vectors, computation of deviation of total enthalpy from its freestream value, as well as formal grid convergence studies. Validation is given Copyright c © 2004 by G. P. Brooks and J. M. Powers. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. This study has received primary support from the United States Air Force Palace Knight Program and additional support from Los Alamos National Laboratory. Research Scientist, Member AIAA. Associate Professor, Associate Fellow AIAA. by showing that shock shape predictions for flow over a sphere are in essential agreement with that observed in experiment. The ability of the method to capture unsteady flow phenomena, including low-amplitude high order harmonics, is demonstrated on the problem of a uni-modal planar acoustic wave interacting with an attached shock and downstream flow field.