Validation of fully implicit, parallel finite element simulations of laminar hypersonic flows

This paper concerns comparative studies of predictive simulations and experimental results from the literature for high-Mach-number two-dimensional/axisymmetric flow past a hollow-cylinder flare and a double cone. The underlying physical model for the mathematical formulation assumes calorically-perfect-gas laminar flow, and we seek to approximate the corresponding compressible Navier-Stokes equations expressed in conservation-variable form. Predictive simulations of this mathematical model are based on a fully implicit, parallel streamline-upwind Petrov-Galerkin finite element formulation that uses a grouped-variable expansion for the inviscid flux terms. The spatial discretization, second-order-accurate time discretization, numerical method, and parallel fully implicit implementation are concisely described. Representative iterative and mesh convergence results are presented for the case of a hollow-cylinder flare. Local predicted values of surface pressure and heat transfer are compared with available experimentally measured values for both geometries. These results are interpreted in the context of validation. Predicted results for complex flowfield/shock interactions and the viscous slip surface are illustrated through a computed schlieren image for the double cone. The present work presents the first known comparison of predictions from the finite element method to this set of data, and the validation study provides the comparative details to motivate future computational investigations and experimental studies.