Adaptive Model Reduction of High-Order Solutions of Compressible Flows via Optimal Transport
Name
Adaptive Model Reduction of High-Order Solutions of Compressible Flows via Optimal Transport.pdf
Description
Published version
Size
7.75 MB
Format
Adobe PDF
Checksum (MD5)
069b930cffd23e1ad84cea9e2ee42d10
Author(s)
Van Heyningen, Robert Loek
Nguyen, Ngoc Cuong
Blonigan, Patrick
Peraire, Jaime
Date Issued
April 28, 2024
Journal
International Journal of Computational Fluid Dynamics
Publisher
Taylor & Francis
Citation
Van Heyningen, R. L., Nguyen, N. C., Blonigan, P., & Peraire, J. (2023). Adaptive Model Reduction of High-Order Solutions of Compressible Flows via Optimal Transport. International Journal of Computational Fluid Dynamics, 37(6), 541–563.
Version
Final published version
Abstract
The solution of conservation laws with parametrised shock waves presents challenges for both high-order numerical methods and model reduction techniques. We introduce an r-adaptivity scheme based on optimal transport and apply it to develop reduced order models for compressible flows. The optimal transport theory allows us to compute high-order r-adaptive meshes from a starting reference mesh by solving the Monge–Ampère equation. A high-order discretization of the conservation laws enables high-order solutions to be computed on the resulting r-adaptive meshes. Furthermore, the Monge–Ampère solutions contain mappings that are used to reduce the spatial locality of the resulting solutions and make them more amenable to model reduction. We use a non-intrusive model reduction method to construct reduced order models of both the mesh and the solution. The procedure is demonstrated on three supersonic and hypersonic test cases, with the hybridisable discontinuous Galerkin method being used as the full order model.
MIT Department
Massachusetts Institute of Technology. Center for Computational Engineering
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivatives
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DOI of Published Version
https://doi.org/10.1080/10618562.2024.2326559
