Evaluation and comparison of modal and nodal Discontinuous Galerkin methods for unsteady simulations of shock-vortex interactions

• A numerical strategy for capturing shock-vortex interactions with Discontinuous Galerkin schemes, including modal DG and nodal DGSEM, is presented • The two schemes are evaluated and compared for an inviscid Mach 3 forward step case, a viscous shock-wall interaction and the supersonic Taylor-Green vortex • In all cases, it is shown that both schemes provide good shock and vortex capturing properties, considering coarse grids, unstructured meshes and high polynomial degrees • DG and DGSEM provide similar solutions on equivalent grids, while DGSEM displays better performance than DG, in particular when considering higher polynomial degrees This paper presents the assessment and comparison of high-order nodal and modal Discontinuous Galerkin schemes for unsteady simulations of freely-developing and wall-bounded scale-resolved shock-turbulence and shock-vortex interaction problems. A numerical strategy that is suitable for both schemes, combining a positivity-preserving limiter, a localized artificial viscosity operator and a turbulence sensor, is presented. This choice of numerical ingredients aims specifically at regularizing shocks while providing a high-accuracy for the representation of vortices and turbulent scales. The accuracy, robustness and performance of the proposed methodologies are assessed in the context of scale-resolved shock-turbulence and shock-vortex interactions considering various resolutions, polynomial degrees and mesh element topology. For all cases considered, it is shown that both schemes provide good shock and vortex capturing properties, even when considering coarse grids, unstructured meshes and high polynomial degrees.