Case 3 . 4 Periodic Hills Re = 10 , 595

This work uses a higher-order discontinuous-Galerkin finite-element method to solve the compressible Navier-Stokes equations [1,2]. The unsteady Navier-Stokes equations are discretized using a non-linearly stable space-time entropyvariable formulation. The inviscid flux is computed using the approximate Riemann solver of Ismail and Roe [3]. The viscous fluxes are computed using an interior penalty (IP) method equivalent to the second form of Bassi and Rebay (BR2) [4]. Evaluation of the integrals appearing in the DG formulation are performed using a dealiased quadrature rule using 2N points in each direction where N is the solution order (in either space or time). The nonlinear problem arising at each time-slab is solved using a Jacobian-free Newton-Krylov method using a diagonalized-ADI preconditioner [5]. Results are presented using the space-time formulation with accuracy up to 16th order (N = 16) in both space and time.