Residual Data-Driven Variational Multiscale Reduced Order Models for Parameter Dependent Problems

TL;DR

This paper introduces a residual-based data-driven closure model within the variational multiscale framework for reduced order models of convection-dominated flows, demonstrating improved accuracy over traditional methods.

Contribution

The paper presents a novel residual-dependent data-driven ROM closure within the VMS framework, enhancing modeling of sub-scale components in convection-dominated problems.

Findings

Residual-based data-driven VMS-ROM outperforms G-ROM and SUPG-ROM in accuracy.

Numerical results validate the effectiveness of the new closure model.

Application to a parameter-dependent convection-diffusion problem demonstrates robustness.

Abstract

In this paper, we investigate the modeling of sub-scale components of proper orthogonal decomposition reduced order models (POD-ROMs) of convection-dominated flows. We propose ROM closure models that depend on the ROM residual. We illustrate the new residual-based data-driven ROM closure within the variational multiscale (VMS) framework and investigate it in the numerical simulation of a one-dimensional parameter-dependent convection-dominated convection-diffusion problem. For comparison purposes, we also investigate a streamline-upwind Petrov-Galerkin (SUPG) ROM stabilization strategy and the standard Galerkin ROM (G-ROM). Our numerical investigation shows that the new residual-based data-driven VMS-ROM is more accurate than both the standard G-ROM and the SUPG-ROM.