Entropy stable reduced order modeling of nonlinear conservation laws using discontinuous Galerkin methods
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915691902271488 |
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| author | Qu, Ray Narayan, Akil Chan, Jesse |
| author_facet | Qu, Ray Narayan, Akil Chan, Jesse |
| contents | Reduced order models (ROMs) are inexpensive surrogate models that reduce costs associated with many-query scenarios. Current methods for constructing entropy stable ROMs for nonlinear conservation laws utilize full order models (FOMs) based on finite volume methods (FVMs). This work describes how to generalize the construction of entropy stable ROMs from FVM FOMs to high order discontinuous Galerkin (DG) FOMs. Significant innovations of our work include the introduction of a new "test basis" which significantly improves accuracy for DG FOMs, a dimension-by-dimension hyper-reduction strategy, and a simplification of the boundary hyper-reduction step based on "Carathéodory pruning". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropy stable reduced order modeling of nonlinear conservation laws using discontinuous Galerkin methods Qu, Ray Narayan, Akil Chan, Jesse Numerical Analysis Reduced order models (ROMs) are inexpensive surrogate models that reduce costs associated with many-query scenarios. Current methods for constructing entropy stable ROMs for nonlinear conservation laws utilize full order models (FOMs) based on finite volume methods (FVMs). This work describes how to generalize the construction of entropy stable ROMs from FVM FOMs to high order discontinuous Galerkin (DG) FOMs. Significant innovations of our work include the introduction of a new "test basis" which significantly improves accuracy for DG FOMs, a dimension-by-dimension hyper-reduction strategy, and a simplification of the boundary hyper-reduction step based on "Carathéodory pruning". |
| title | Entropy stable reduced order modeling of nonlinear conservation laws using discontinuous Galerkin methods |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2502.09381 |