Standardized pseudospectral formulation of the inviscid supsersonic blunt body problem

• Authors: Gregory P. Brooks;Joseph M. Powers
• Venue: Journal of Computational Physics
• Year: 2004

A highly accurate pseudospectral numerical approximation to the generalized coordinate, nonconservative form of the Euler equations is implemented for supersonic flow over an axisymmetric blunt body geometry; shock fitting is employed to maintain global accuracy and minimize the corrupting influence of numerical viscosity. The variables in the Euler equations as well as the physical grid coordinates are collocated via Lagrange interpolating polynomials and the problem is then cast in the standard form of a large system of ordinary differential equations, dx/dτ = q(x), which can be solved using standard solution techniques that do not require an explicit criteria for the minimum time step. Code verification is performed by demonstrating through a series of grid refinement tests that the error in the approximation to a Taylor-Maccoll solution converges to 10-12. Grid refinement tests for flow over a blunt body show convergence of the numerical error also to 10-12. The code is validated for supersonic flow over a blunt body by comparison with the modified Newtonian approximation for the surface pressure distribution and empirical predictions for the shock shape. The ability of the method to capture unsteady flow phenomena is demonstrated on the problem of a planar acoustic wave interacting with an attached shock.