Moving Discontinuous Galerkin Solver for Hypersonic Aerothermodynamics

Corvid Technologies (Corvid) and North Carolina State University (NCSU) are employing a novel moving Discontinuous Galerkin with Interface Conservation Enforcement (MDG+ICE) approach. The MDG+ICE method represents a fundamentally grounded and break-through approach and is specifically designed for flows with discontinuities and therefore especially attractive for hypersonic flows. During Phase I, Corvid and NCSU developed and demonstrated a compressible Euler solver with thermochemical nonequilibrium models based on the MDG+ICE approach. High order capabilities were developed to enable solutions up to P2 (third-order accurate) on quadratic (curved) elements. This new approach was shown to capture shocks (discontinuities) and the associated jumps in thermodynamic properties exactly, while using a fraction of the grid cells typically used in second-order solvers. MDG2D was verified on several 1-D shock tube problems, as well as steady 2-D problems with a 5-species, 2 temperature air chemistry model. Excellent agreement was demonstrated when comparing to NASArsquo;s state-of-the-art codes DPLR and LAURA for 2-D blunt bodies in hypersonic flows. This work represents the first time any group has applied the moving Discontinuous Galerkin approach for a reacting mixture of gases with two temperatures. Based on this success, our efforts in Phase II will be focused on developing a prototype software (MDGFLO) based on the MDG+ICE approach to solve the compressible Navier-Stokes equations with thermal and chemical nonequilibrium, in three dimensions on massively parallel computing systems. In particular, we will investigate if the MDG+ICE method can be effectively used for accurately computing both hypersonic heating and after-body flow field and validate it against available test data.