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This is a Human Clinical Trial study (also classified as: RCT, Observational).

September 10, 2025

HDG methods for incompressible and immiscible two-phase flow in porous media: the existence and convergence of discrete solutions

Key Points

The discrete solution for the proposed scheme exists, indicating that the numerical method is valid.
Established using the Brouwer fixed-point theorem, the method confirms convergence to a weak solution of the continuous problem.
Two numerical examples demonstrate both accuracy and performance of the HDG method in modeling two-phase flow.
Results support the feasibility of using HDG methods for incompressible and immiscible flow in porous media, highlighting potential applications.

Abstract

In this paper, we investigate the numerical approximation of incompressible, immiscible two-phase flow in porous media using backward Euler methods for time discretization and hybridized discontinuous Galerkin (HDG) methods for saturation and pressure discretizations. Using the Brouwer fixed-point theorem, we establish the existence of a discrete solution for the proposed scheme. Furthermore, the sequence of discrete solutions solved by the discrete scheme converges, potentially after passing to a subsequence, to a weak solution of the continuous problem. Finally, two numerical examples are presented to validate both the accuracy and performance of the discrete scheme.

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