Variational Multiscale Proper Orthogonal Decomposition: Convection-Dominated Convection-Diffusion Equations

TL;DR

This paper presents a variational multiscale closure approach to stabilize proper orthogonal decomposition reduced-order models for convection-dominated convection-diffusion equations, improving accuracy and convergence.

Contribution

It introduces a novel variational multiscale closure method specifically designed for POD models in convection-dominated problems, with theoretical analysis and numerical validation.

Findings

Enhanced numerical accuracy over standard POD models

Theoretical convergence rates confirmed by numerical tests

Effective stabilization for convection-dominated equations

Abstract

We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested for convection-dominated convection-diffusion equations. The numerical analysis of the finite element discretization of the model is presented. Numerical tests show the increased numerical accuracy over the standard reduced-order model and illustrate the theoretical convergence rates.