An energy stable and mass-conservative numerical method for gas flow in poroelastic media

Abstract

In this paper, we develop an efficient numerical method to solve a thermodynamically consistent gas flow model in porous media with compressible gas and rock. Since the model is strongly nonlinear and fully coupled, it is difficult to design numerical methods that satisfy the energy dissipation law. We employ a stabilization method to design a time semi-discrete scheme that is weakly nonlinear and satisfies the energy dissipation law. The fully discrete scheme is constructed using the discontinuous Galerkin (DG) and mixed finite element methods with the upwind strategy. The fully discrete scheme is proven to satisfy the laws of mass conservation and energy dissipation. Numerical results are also provided to show the performance of the proposed scheme and validate the theoretical analysis.

Cited as: Chen, H., Chen, Y., Kou, J. An energy stable and mass-conservative numerical method for gas flow in poroelastic media. Computational Energy Science, 2024, 1(2): 86-101. https://doi.org/10.46690/compes.2024.02.03

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