Reduced Order Modeling of Hypersonic Boundary Layers using Data Informed Local Subspaces

Design of future hypersonic vehicles and weapons systems will require detailed, trajectory-level modeling of complex multiphysics systems over a large span of parameters. The fluid component of these multiphysics systems is extremely difficult and computationally expensive to simulate, rendering a modeling approach based solely on high-fidelity simulation infeasible. In this STTR project, RNET Technologies, Florida Atlantic University, and Florida State University will use a novel Data-defined Local Subspaces (DLS) technique to develop efficient and scalable reduced-order-models (ROMs) of hypersonic boundary layers.Our novel DLS-ROM approach uses partition-of-unity models is defined in an ultra-low resolution enriched finite elements space to significantly reduce computational cost when compared against direct numerical simulation approaches. Encorperating modern machine learning techniques within a robust generalized finite element formulation, this effort will target an order of magnitude in cost reduction while still maintaining a level of accuracy consistent with that achievable through direct numerical simulation.The DLS-ROM approach will advance the state-of-the-art by 1) leveraging C0 continuity at cell boundaries to eliminate the need for flux matching or boundary condition passing at ``component boundaries''; 2) learning spatially local features that generalize to changes in parameters and geometries, and 3) using adaptive local basis selection to enable data-driven hyper-reduction.In this Phase I STTR project, RNET, FAU, and FSU will use their combined expertise in aerothermodynamics simulation, reduced order modeling, and high-performance computing to demonstrate the feasibility DLS based ROMs. This feasibility demonstration will focus on developing, profiling, and analyzing our DLS-ROM approach for compressible Navier-Stokes flow of an ideal gas over single-cone, double-cone, and cone-cylinder-flare geometries. The effort will include a detailed report on the accuaracy, performance and memory usage of these DLS-ROMs when compared against direct numerical simulation and the state-of-the-art in component based reduced order modeling.The Phase I effort will demonstrate technical feasibility by applying DLS ROM methods to high Reynolds number flow over a 60 degree section of a cone-cylinder-flare under an ideal-gas assumption. In Phase II, the Phase I prototype will be extended to support the entire cone-cylinder-flare geometry, and to support chemical and thermal non-equilibrium in the gas, under relevant flight conditions. The Phase 1 prototype will be TRL 3/4, as the algorithms will be implemented and functionality will be demonstrated on a representative problem. The Phase 2 software will be TRL 6/7, and will be validated against experiments and/or full scale WR-LES datasets.