A numerical study of hypersonic stagnation heat transfer predictions at a coordinate singularity

The problem of grid induced errors associated with a coordinate singularity on heating predictions in the stagnation region of a three-dimensional body in hypersonic flow is examined. The test problem is for Mach 10 flow over an Aeroassist Flight Experiment configuration. This configuration is composed of an elliptic nose, a raked elliptic cone, and a circular shoulder. Irregularities in the heating predictions in the vicinity of the coordinate singularity, located at the axis of the elliptic nose near the stagnation point, are examined with respect to grid refinement and grid restructuring. The algorithm is derived using a finite-volume formulation. An upwind-biased total-variation diminishing scheme is employed for the inviscid flux contribution, and central differences are used for the viscous terms.