A cell centered Galerkin method for miscible displacement in heterogeneous porous media

2025-09-18

AI Summary

This work addresses the challenge of efficient numerical simulation of miscible displacement in heterogeneous porous media. We propose a cell-centered Galerkin (CCG) method that innovatively combines the discontinuous Galerkin (DG) weak formulation with finite-volume principles, introducing only one degree of freedom per element while rigorously enforcing local mass conservation. In one dimension, we prove that the resulting discrete system matrix is inverse-positive. Compared to conventional high-order DG methods, CCG achieves comparable accuracy at significantly reduced computational cost. Extensive two- and three-dimensional numerical experiments demonstrate that the method remains stable, efficient, and accurate even under strong heterogeneity. By offering low degrees of freedom and high robustness, CCG establishes a new paradigm for large-scale miscible displacement simulation.

Technology Category

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Abstract

In this paper we present a cell centered Galerkin (CCG) method applied to miscible displacement problems in heterogeneous porous media. The CCG approach combines concepts from finite volume and discontinuous Galerkin (DG) methods to arrive at an efficient lowest-order approximation (one unknown per cell). We demonstrate that the CCG method can be defined using classical DG weak formulations, only requires one unknown per cell, and is able to deliver comparable accuracy and improved efficiency over traditional higher-order interior penalty DG methods. In addition, we prove that the CCG method for a model Poisson problem gives rise to a inverse-positive matrix in 1D. A plethora of computational experiments in 2D and 3D showcase the effectiveness of the CCG method for highly heterogeneous flow and transport problems in porous media. Comparisons between CCG and classical DG methods are included.

Problem

• Develops cell-centered Galerkin method for miscible displacement
• Solves flow in heterogeneous porous media problems
• Improves efficiency over traditional higher-order DG methods

Innovation

• Cell centered Galerkin method combining finite volume
• Uses one unknown per cell for efficiency
• Delivers comparable accuracy to higher-order methods