High-order finite-element method for three-dimensional turbulent Navier-Stokes

In this paper a high-order streamline/upwind Petrov-Galerkin (SUPG) finite element discretization is investigated and developed for solutions of three-dimensional turbulent flows. The modified Spalart and Allmaras (SA) turbulence model is implemented and is discretized consistently with the main Reynolds Averaged Navier-Stokes (RANS) equations using the high-order finite element scheme. The present method treats the discretized system fully implicitly to obtain steady state solutions or to drive unsteady problems at each time step. To accurately represent the geometries, high-order curved boundary meshes are generated via a CAPRI interface, while the interior meshes are deformed through a linear elasticity solver. This procedure effectively prevents the generation of collapsed elements due to the projection of the curved physical boundaries and thus allows high-aspect-ratio curved elements in viscous boundary layers. Several numerical examples, including viscous flow over a three-dimensional cylinder and flow over an ONERA M6 swept wing are presented and compared with a discontinuous-Galerkin method. Finally, solutions are obtained for a high-lift multi-element wing to demonstrate the capability of the high-order finite element solver.