Fluid flow and solute transport in fractured porous media is the backbone of many applications including groundwater flow, underground energy harvesting, earthquake prediction, and biomedical engineering. The traditional continuous Galerkin (CG) method is not suitable for the transport equation due to lack of mass conservation. The discontinuous Galerkin (DG) method mitigates this problem; however, its computational cost is considerably more than the CG method. In this study, a robust and efficient discretization method based on the incomplete interior penalty enriched Galerkin (EG) method is proposed. This method requires fewer degrees of freedom than those of the DG method, while it achieves the same accuracy. The flow and transport models of rock matrix and fractures domains are investigated in the mixed-dimensional setting. The results of combinations of function spaces, for example, (i) CG × CG, (ii) CG × EG, and (iii) CG × DG spaces are compared. The results illustrate the superiority of the EG and DG methods in solving the flow and transport equations in fractured porous media. Furthermore, the computational burden of the EG method is two times cheaper than that of the DG method.
|Publication status||Published - 2019|
|Event||FEniCS'19 - Carnegie Institution for Science Department of Terrestrial Magnetism, Washington DC, United States|
Duration: 12 Jun 2019 → 14 Jun 2019
|Location||Carnegie Institution for Science Department of Terrestrial Magnetism|
|Period||12/06/2019 → 14/06/2019|
Kadeethum, T., Nick, H., Richardson, C. N., Ballarin, F., & Lee, S. (2019). Enriched Galerkin Discretization for Modelling Flow in Fractured Porous Media using Mixed-Dimensional Approach. Abstract from FEniCS'19, Washington DC, United States.