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 NASAs 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. Computational modeling of hypersonic flows is now more important than ever with the recent push in hypersonic technologies in the National Aeronautics and Space Administration (NASA) and in the defense industry. The state-of-the-art computational fluid dynamic (CFD) capabilities, however, still have many limitations in terms of accuracy, fidelity, and robustness which need to be addressed. In response to this need, 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. This capability would enable a faster turn-around for modeling the complex physics relevant to entry-type problems due to increased robustness, higher order numerics less sensitive to mesh topologies and resolutions, and flexibility afforded by unstructured grids. During the Phase II effort, our team will work to meet the primary objectives of this research which include 1) extending the MDG+ICE approach to 3-D viscous flows in thermochemical nonequilibrium, 2) improving the computational efficiency of MDG+ICE approach, 3) developing an MDG+ICE Navier-Stokes prototype software, and 4) validating the performance of MDGFLO solver for hypersonic applications Deliverables for this effort include a kickoff meeting within 30 days of contract start, a quarterly progress report every three months, a copy of the prototype software developed (MDGFLO) including documentation and sample cases, and a final report.

The proposed solution would directly benefit all of NASA’s on-going and upcoming EDL programs by delivering a high-order, robust CFD modeling capability for reentry modeling. Programs include Orion, Mars sample return, Mars2020, deployable heatshield programs (HIAD, ADEPT), and planetary missions. This capability would also greatly improve the fidelity and turn-around times for modeling of the different spacecraft being developed by NASA’s commercial partners such as SpaceX, Boeing, and Sierra Nevada. The proposed solution would also greatly benefit the Defense Industry. Applications in the Army, Navy, Air Force and Missile Defense Agency, as well as the large defense prime contractors such as Raytheon, Lockheed Martin, Boeing, and Northrop Grumman could use the CFD capabilities developed in this work.

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