Entropy stable reduced order modeling of nonlinear conservation laws

TL;DR

This paper introduces a new class of reduced order models for nonlinear conservation laws in fluid dynamics that are both globally conservative and entropy stable, regardless of basis or parameters.

Contribution

The authors develop projection-based hyper-reduced models that ensure stability and conservation properties are maintained in reduced order modeling.

Findings

Models are globally conservative.

Models inherit semi-discrete entropy inequalities.

Stability is independent of basis and parameters.

Abstract

Reduced order models of nonlinear conservation laws in fluid dynamics do not typically inherit stability properties of the full order model. We introduce projection-based hyper-reduced models of nonlinear conservation laws which are globally conservative and inherit a semi-discrete entropy inequality independently of the choice of basis and choice of parameters.