Abstract
This work considers the use of a family of compact discontinuous Galerkin (DG) methods to simulate unsteady hypersonic inviscid ow over a blunt body and compare the solution quality at a xed resolution. These ow conditions give rise to shocks that, mathematically speaking, are discontinuities. The presence of shocks and small-scale ow features lead to challenging numerical simulation. In particular, we assess the scheme's performance for standard benchmark tests while varying the shock-capturing limiter, numerical ux, and the scheme's order. In particular, we consider the classical Minmod limiter, its high-order generalization(s), and a recently introduced moment-based limiter by Moe, Rossmanith, and Seal. To couple our quadrilateral sub-domains we consider the popular Lax Friedrichs numerical ux, as well as the HLL, Roe, and Marquina numerical uxes. Our simulations are carried out using a newly developed partial dierential equation solver, SpECTRE, that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE has been developed for solving astrophysics problems, while the work described here focuses on problems in Mechanical and Aerospace Engineering. As such, we also document the additional functionality that was implemented as part of this work, including how to handle solid objects and wall-type boundary conditions. We will also briey touch on the SpECTRE's scalability on MGHPCC machine that has been used extensively throughout the completion of this work.