Verification and validation for laminar hypersonic flowfields, part 1: Verification

Numerical simulations are performed for Mach 8 laminar flow of a calorically perfect gas over a spherically blunted cone. Code verification calculations are conducted to provide confidence that there are no coding mistakes and include comparisons to highly accurate inviscid benchmark solutions as well as code-to-code comparisons. Special attention is paid to the numerical accuracy of the solutions by carefully monitoring iterative convergence errors and by conducting an extensive grid convergence study. Nonmonotonic convergence of the surface pressure and drag are observed with mesh refinement. The source of this nonmonotonicity is explored in detail. The standard method for determining the spatial order of accuracy is shown to be inadequate for the numerical algorithm employed, and an alternative method is proposed. The overall discretization error of the fine grid surface pressure distributions is estimated to be below 0.4%, with the maximum errors found at the sphere-cone tangency point. With the accuracies demonstrated, it is recommended that the present computations can be used as a numerical benchmark solution for code verification.