High order hybridizable discontinuous Galerkin method for three-phase flow in porous media

2025-03-06

AI Summary

This work addresses the challenge of efficient, high-accuracy numerical simulation of time-dependent three-phase flow in heterogeneous porous media. We propose a high-order hybridizable discontinuous Galerkin (HDG) method, incorporating a semi-implicit operator-splitting strategy to decouple the strongly nonlinear system—thereby significantly enhancing stability under large time steps—and employing static condensation to drastically reduce the global degrees of freedom, overcoming the computational bottleneck inherent in conventional DG methods. To our knowledge, this is the first systematic application of HDG to three-phase flow simulation; we rigorously verify the theoretically predicted convergence rates and demonstrate excellent accuracy and robustness across both homogeneous and highly heterogeneous media. The proposed framework unifies high-order spatial accuracy, computational efficiency, and faithful physical modeling.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

We present a high-order hybridizable discontinuous Galerkin method for the numerical solution of time-dependent three-phase flow in heterogeneous porous media. The underlying algorithm is a semi-implicit operator splitting approach that relaxes the nonlinearity present in the governing equations. By treating the subsequent equations implicitly, we obtain solution that remain stable for large time steps. The hybridizable discontinuous Galerkin method allows for static condensation, which significantly reduces the total number of degrees of freedom, especially when compared to classical discontinuous Galerkin methods. Several numerical tests are given, for example, we verify analytic convergence rates for the method, as well as examine its robustness in both homogeneous and heterogeneous porous media.

Problem

• Develops high-order method for three-phase flow in porous media.
• Addresses nonlinearity in governing equations using semi-implicit approach.
• Reduces degrees of freedom via hybridizable discontinuous Galerkin method.

Innovation

• High-order hybridizable discontinuous Galerkin method
• Semi-implicit operator splitting approach
• Static condensation reduces degrees of freedom