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

TL;DR

This paper develops a method to create entropy stable reduced order models for nonlinear conservation laws using high order discontinuous Galerkin methods, improving accuracy and efficiency over existing finite volume-based approaches.

Contribution

It introduces a new test basis, a dimension-by-dimension hyper-reduction strategy, and simplifies boundary hyper-reduction for DG-based entropy stable ROMs.

Findings

Enhanced accuracy with the new test basis

Reduced computational cost through hyper-reduction strategies

Simplified boundary hyper-reduction process

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 "Carath\'eodory pruning".