Three-Dimensional Stabilized Finite Elements for Compressible Navier–Stokes

In this paper, a stabilized finite-element approach is used in the development of a high-order flow solver for compressible flows. The streamline/upwind Petrov–Galerkin discretization is used for the Navier–Stokes equations, and a fully implicit methodology is used for advancing the solution at each time step. The order of accuracy is assessed for both inviscid and viscous flows using the method of manufactured solutions. For two-dimensional flow, a mesh-curving strategy is discussed that allows high-aspect-ratio curved elements in viscous flow regions. In addition, the effects of curved elements are evaluated in two dimensions using the method of manufacture solutions. Finally, test cases are presented in two and three dimensions and compared with well-established results and/or experimental data.