Entropy stable reduced order modeling of nonlinear conservation laws using discontinuous Galerkin methods

2025/02/13 by R. Qu, Qu, Ray, Akil Narayan +3 · 1 citation
Engineering · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2502.09381

openalex publication_date 2025/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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".

Cited by

• Efficient and Robust Carathéodory-Steinitz Pruning of Positive Discrete Measures

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