Proper orthogonal decomposition closure models for fluid flows: Burgers equation

TL;DR

This paper introduces new closure models for POD reduced order modeling of fluid flows, tested on Burgers equation with moving shock waves, assessing accuracy and efficiency.

Contribution

It proposes several novel closure models for POD reduced order models and evaluates their performance on Burgers equation with shock waves.

Findings

New closure models improve accuracy over standard models.

Models show good computational efficiency.

Performance varies with parameter sensitivity.

Abstract

This paper puts forth several closure models for the proper orthogonal decomposition (POD) reduced order modeling of fluid flows. These new closure models, together with other standard closure models, are investigated in the numerical simulation of the Burgers equation. This simplified setting represents just the first step in the investigation of the new closure models. It allows a thorough assessment of the performance of the new models, including a parameter sensitivity study. Two challenging test problems displaying moving shock waves are chosen in the numerical investigation. The closure models and a standard Galerkin POD reduced order model are benchmarked against the fine resolution numerical simulation. Both numerical accuracy and computational efficiency are used to assess the performance of the models.