Development and validation of a SUPG finite element scheme for the compressible Navier-Stokes equations using a modified inviscid flux discretization

This paper considers the streamline-upwind Petrov-Galerkin (SUPG) method applied to the unsteady compressible Navier-Stokes equations in conservation-variable form. The spatial discretization, including a modified approach for interpolating the inviscid flux terms in the SUPG finite element formulation, and the second-order accurate time discretization are presented. The numerical method is discussed in detail. The performance of the algorithm is then investigated by considering inviscid flow past a circular cylinder. Validation of the finite element formulation via comparisons with experimental data for high-Mach number perfect gas laminar flows is presented, with a specific focus on comparisons with experimentally measured skin friction and convective heat transfer on a 15° compression ramp.