Implementation of High Order Discontinuous Galerkin Method and Its Verification Using Taylor-Green Vortex and Periodic Hills Test Cases

An implementation of Discontinuous Galerkin method designed for unsteady computations is presented. Explicit 4-th order 5-stage strong stability-preserving Runge-Kutta scheme is used together with global time stepping technique. Shape functions are taken to be orthonormal polynomials in physical space. Polynomial orders K of up to 5 are used, formally giving a K + 1 accuracy order. Bassi and Rebay 2 approximation of viscous fluxes is adopted. Test cases presented are DNS of Taylor-Green Vortex at Re = 1600 and ILES/DDES computations of ERCOFTAC Periodic Hills test case at Re = 10 595. The results include accuracy versus computational cost comparisons.