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

TL;DR

This paper compares dynamic mode decomposition and proper orthogonal decomposition for modeling flows in high-contrast porous media, highlighting DMD's superior long-term predictive capabilities and analyzing their robustness under various conditions.

Contribution

It demonstrates the effectiveness of DMD and POD in capturing flow dynamics in heterogeneous media and assesses their robustness and limitations.

Findings

DMD better predicts long-term flow evolution.

DMD effectively captures slowly-decaying eigenmodes.

Both methods' robustness varies with initial conditions and permeability variations.

Abstract

We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) methods to flows in highly-heterogeneous porous media to extract the dominant coherent structures and derive reduced-order models via Galerkin projection. Permeability fields with high contrast are considered to investigate the capability of these techniques to capture the main flow features and forecast the flow evolution within a certain accuracy. A DMD-based approach shows a better predictive capability due to its ability to accurately extract the information relevant to long-time dynamics, in particular, the slowly-decaying eigenmodes corresponding to largest eigenvalues. Our study enables a better understanding of the strengths and weaknesses of the applicability of these techniques for flows in high-contrast porous media. Furthermore, we discuss the robustness of DMD- and POD-based reduced-order models with respect to variations in initial conditions, permeability fields, and forcing terms.