An Energy-Stable, Bound-Preserving and Locally Conservative Numerical Framework for Multicomponent Gas Flow in Poroelastic Media

TL;DR

This paper introduces a novel numerical framework for multicomponent gas flow in poroelastic media that ensures energy stability, bound preservation, and local mass conservation, improving reliability and efficiency in simulations.

Contribution

The paper develops a stabilized discretization method combining mixed finite elements, upwind schemes, and DG methods, with adaptive time-stepping for robust, accurate, and efficient simulations.

Findings

The method guarantees energy dissipation and molar density bounds.

Numerical experiments confirm robustness and accuracy.

Adaptive time-stepping enhances computational efficiency.

Abstract

In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The model captures the complex nonlinear coupling between multicomponent transport and solid deformation, while addressing critical numerical challenges such as mass conservation, energy stability, and molar density boundedness. To achieve this, we develop a stabilized discretization approach that guarantees the preservation of the original energy dissipation law and ensures the boundedness of each gas component's molar density. Furthermore, the proposed method incorporates an adaptive time-stepping strategy that dynamically adjusts the time step size based on the system's dynamics, significantly enhancing computational efficiency without compromising stability or accuracy. For spatial discretization, a mixed finite element method combined with an upwind scheme is employed for the flow and transport equations to ensure local mass conservation, while a discontinuous Galerkin (DG) method is utilized for discretizing the momentum equation of poroelasticity to effectively overcome numerical locking phenomena. Numerical experiments are presented to demonstrate the performance, robustness, and applicability of the method in simulating multicomponent gas flow under various scenarios.