Veri cation and Validation for Laminar Hypersonic Flow elds, Part 1: Veri cation

Numerical simulations are performed for Mach 8 laminar ow of a calorically perfect gas over a spherically blunted cone. Code veri cation calculations are conducted to provide con dence that there are no codingmistakes 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. Nonmonotonicconvergence of the surface pressure anddrag are observedwithmesh re nement. The source of this nonmonotonicityis 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 alternativemethod is proposed. The overall discretization error of the ne 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 veri cation. Nomenclature f = solution variable gi = i th-order error term coef cient h = measure of the grid cell spacing M = Mach number N = total number of grid cell