Nonintrusive reduced order modeling of convective Boussinesq flows

TL;DR

This paper compares three nonintrusive reduced order modeling methods—DMD, randomized DMD, and NLPOD—for convective Boussinesq flows, highlighting their reconstruction accuracy, predictive capabilities, and robustness to noise.

Contribution

It systematically evaluates the performance of three nonintrusive ROM methods on convection-dominated flows, revealing NLPOD's superior robustness to noise.

Findings

All three methods accurately predict flow quantities with proper mode selection.

NLPOD demonstrates greater robustness under high noise conditions.

Predictions closely match full order model solutions.

Abstract

In this paper, we formulate three nonintrusive methods and systematically explore their performance in terms of the ability to reconstruct the quantities of interest and their predictive capabilities. The methods include deterministic dynamic mode decomposition (DMD), randomized DMD and nonlinear proper orthogonal decomposition (NLPOD). We apply these methods to a convection dominated fluid flow problem governed by the Boussinesq equations. We analyze the reconstruction results primarily at two different times for considering different noise levels synthetically added into the data snapshots. Overall, our results indicate that, with a proper selection of the number of retained modes and neural network architectures, all three approaches make predictions that are in a good agreement with the full order model solution. However, we find that the NLPOD approach seems more robust for higher noise levels compared to both DMD approaches.