A Priori Error Bounds for the Approximate Deconvolution Leray Reduced Order Model

TL;DR

This paper establishes the first a priori error bounds for the approximate deconvolution Leray reduced order model (ADL-ROM), demonstrating its stability and accuracy improvements in convection-dominated flow simulations.

Contribution

It provides the first numerical analysis of approximate deconvolution within a reduced order model framework, enhancing understanding of ADL-ROM's theoretical properties.

Findings

ADL-ROM is more stable than standard ROM in convection-dominated flows.

ADL-ROM achieves higher accuracy than Leray ROM.

Numerical simulations confirm the theoretical error bounds.

Abstract

The approximate deconvolution Leray reduced order model (ADL-ROM) uses spatial filtering to increase the ROM stability, and approximate deconvolution to increase the ROM accuracy. In the under-resolved numerical simulation of convection-dominated flows, ADL-ROM was shown to be significantly more stable than the standard ROM, and more accurate than the Leray ROM. In this paper, we prove a priori error bounds for the approximate deconvolution operator and ADL-ROM. To our knowledge, these are the first numerical analysis results for approximate deconvolution in a ROM context. We illustrate these numerical analysis results in the numerical simulation of convection-dominated flows.