Approximate Deconvolution Leray Reduced Order Model for Convection-Dominated Flows

TL;DR

This paper introduces the ADL-ROM, a stabilized reduced order model for convection-dominated flows that enhances accuracy and stability using approximate deconvolution techniques, including Tikhonov and van Cittert methods.

Contribution

It proposes a novel ADL-ROM with new deconvolution strategies that improve accuracy and robustness over classical models for convection-dominated flows.

Findings

ADL-ROM outperforms L-ROM in accuracy when the filter radius is large.

ADL-ROM is less sensitive to model parameters than L-ROM.

The new strategies enhance stability and precision in convection-dominated flow simulations.

Abstract

In this paper, we propose a novel ROM stabilization strategy for under-resolved convection-dominated flows, the approximate deconvolution Leray ROM (ADL-ROM). The new ADL-ROM introduces AD as a new means to increase the accuracy of the classical Leray ROM (L-ROM) without degrading its numerical stability. We also introduce two new AD ROM strategies: the Tikhonov and van Cittert methods. Our numerical investigation for convection-dominated systems shows that, when the filter radius is relatively large, the new ADL-ROM is more accurate than the standard L-ROM. Furthermore, the new ADL-ROM is less sensitive with respect to model parameters than L-ROM.