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. Furthermore, the procedure is demonstrated on three supersonic and hypersonic test cases, with the hybridisable discontinuous Galerkin method being used as the full order model.
Van Heyningen, Robert Loek, et al. "Adaptive Model Reduction of High-Order Solutions of Compressible Flows via Optimal Transport." International Journal of Computational Fluid Dynamics, vol. 37, no. 6, Apr. 2024. https://doi.org/10.1080/10618562.2024.2326559
Van Heyningen, Robert Loek, Nguyen, Ngoc Cuong, Blonigan, Patrick Joseph, & Peraire, Jaime (2024). Adaptive Model Reduction of High-Order Solutions of Compressible Flows via Optimal Transport. International Journal of Computational Fluid Dynamics, 37(6). https://doi.org/10.1080/10618562.2024.2326559
Van Heyningen, Robert Loek, Nguyen, Ngoc Cuong, Blonigan, Patrick Joseph, et al., "Adaptive Model Reduction of High-Order Solutions of Compressible Flows via Optimal Transport," International Journal of Computational Fluid Dynamics 37, no. 6 (2024), https://doi.org/10.1080/10618562.2024.2326559
@article{osti_2341682,
author = {Van Heyningen, Robert Loek and Nguyen, Ngoc Cuong and Blonigan, Patrick Joseph and Peraire, Jaime},
title = {Adaptive Model Reduction of High-Order Solutions of Compressible Flows via Optimal Transport},
annote = {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. Furthermore, the procedure is demonstrated on three supersonic and hypersonic test cases, with the hybridisable discontinuous Galerkin method being used as the full order model.},
doi = {10.1080/10618562.2024.2326559},
url = {https://www.osti.gov/biblio/2341682},
journal = {International Journal of Computational Fluid Dynamics},
issn = {ISSN 1061-8562},
number = {6},
volume = {37},
place = {United States},
publisher = {Taylor & Francis},
year = {2024},
month = {04}}