Mode Decomposition Methods for Flows in High-Contrast Porous Media. Part II. Local-Global Approach

TL;DR

This paper introduces a combined local-global model reduction method using POD and DMD for simulating flows in high-contrast porous media, significantly reducing computational complexity while maintaining accuracy.

Contribution

It develops a novel local-global approach integrating POD and DMD with multiscale finite element methods for efficient flow simulation in high-contrast media.

Findings

Significant reduction in flow problem size

Accurate capture of fully resolved solutions

Effective handling of high-contrast coefficients

Abstract

In this paper, we combine concepts of the generalized multiscale finite element method and mode decomposition methods to construct a robust local-global approach for model reduction of flows in high-contrast porous media. This is achieved by implementing proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques on a coarse grid. The resulting reduced-order approach enables a significant reduction in the flow problem size while accurately capturing the behavior of fully resolved solutions. We consider a variety of high-contrast coefficients and present the corresponding numerical results to illustrate the effectiveness of the proposed technique. This paper is a continuation of the first part where we examine the applicability of POD and DMD to derive simplified and reliable representations of flows in high-contrast porous media. In the current paper, we discuss how these global model reduction approaches can be combined with local techniques to speed-up the simulations. The speed-up is due to inexpensive, while sufficiently accurate, computations of global snapshots.