Adaptive high-order methods and reduced-order models for hypersonic flow via optimal transport
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vanHeyningen-rloekvh-phd-AA-CSE-2025.pdf
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17.7 MB
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Author(s)
Van Heyningen, Robert Loek
Advisor(s)
Peraire, Jaime
Nguyen, Ngoc Cuong
Date Issued
February 2026
Publisher
Massachusetts Institute of Technology
Abstract
Predicting flow conditions in hypersonic environments is central to the scientific goal of improving our understanding of high-speed flows and to practical tasks like the design of hypersonic vehicles. The experimental data needed to elucidate the extreme conditions brought about by flow at such high speeds is difficult both to obtain and appropriately characterize. While computational methods can supplement and help interpret scarce experimental data, these same environments are challenging to simulate. Even if a robust high-fidelity simulation can be run in isolation, it is often too expensive to be run in a many-query context that requires multiple simulations at different operating parameters. Surrogate models can make these workflows more tractable, but parametrized high-speed flows often strain traditional surrogate modeling techniques. This thesis presents several advances in the fields of high-fidelity simulation and surrogate construction for hypersonic flows. Both approaches rely on a novel mesh adaptation technique based on optimal transport theory. We demonstrate high-order methods for problems with shocks, viscous effects, and realistic hypersonic modeling terms describing chemical nonequilibrium. This is accomplished by combining the optimal transport mesh adaptation procedure with an artificial viscosity continuation method that efficiently solves steady-state problems and stabilizes high-order methods in the presence of strong shocks. For surrogate model construction, we use the solutions of the flow and the corresponding grid deformations to learn reduced-order models for solution fields and mesh mappings. This approach is shown to be effective for problems with parametrically varying shocks, a necessity for dealing with parametrized blunt body flows. Finally, we couple these approaches with novel projection-based reduced-order models of hybridizable discontinuous Galerkin discretizations.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Center for Computational Science and Engineering
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