Work

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

Year: 2025

Type: article

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.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2025074

Authors: Haitao Leng, Huangxin Chen

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funders: National Natural Science Foundation of China, Basic and Applied Basic Research Foundation of Guangdong Province

Awards: G1246681862, G3215464590, G5835633742, G997149492