Enriched Galerkin Discretization for Modelling Flow in Fractured Porous Media using Mixed-Dimensional Approach

Teeratorn Kadeethum, Hamid Nick, C. N. Richardson, F. Ballarin, S. Lee

Research output: Contribution to conferenceConference abstract for conferenceResearchpeer-review

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Abstract

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.
Original languageEnglish
Publication date2019
Publication statusPublished - 2019
EventFEniCS'19 - Carnegie Institution for Science Department of Terrestrial Magnetism, Washington DC, United States
Duration: 12 Jun 201914 Jun 2019
https://fenicsproject.org/fenics19/

Conference

ConferenceFEniCS'19
LocationCarnegie Institution for Science Department of Terrestrial Magnetism
CountryUnited States
CityWashington DC
Period12/06/201914/06/2019
Internet address

Cite this

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.
Kadeethum, Teeratorn ; Nick, Hamid ; Richardson, C. N. ; Ballarin, F. ; Lee, S. / Enriched Galerkin Discretization for Modelling Flow in Fractured Porous Media using Mixed-Dimensional Approach. Abstract from FEniCS'19, Washington DC, United States.
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abstract = "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.",
author = "Teeratorn Kadeethum and Hamid Nick and Richardson, {C. N.} and F. Ballarin and S. Lee",
year = "2019",
language = "English",
note = "FEniCS'19 ; Conference date: 12-06-2019 Through 14-06-2019",
url = "https://fenicsproject.org/fenics19/",

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Kadeethum, T, Nick, H, Richardson, CN, Ballarin, F & Lee, S 2019, 'Enriched Galerkin Discretization for Modelling Flow in Fractured Porous Media using Mixed-Dimensional Approach', FEniCS'19, Washington DC, United States, 12/06/2019 - 14/06/2019.

Enriched Galerkin Discretization for Modelling Flow in Fractured Porous Media using Mixed-Dimensional Approach. / Kadeethum, Teeratorn; Nick, Hamid; Richardson, C. N.; Ballarin, F.; Lee, S.

2019. Abstract from FEniCS'19, Washington DC, United States.

Research output: Contribution to conferenceConference abstract for conferenceResearchpeer-review

TY - ABST

T1 - Enriched Galerkin Discretization for Modelling Flow in Fractured Porous Media using Mixed-Dimensional Approach

AU - Kadeethum, Teeratorn

AU - Nick, Hamid

AU - Richardson, C. N.

AU - Ballarin, F.

AU - Lee, S.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

M3 - Conference abstract for conference

ER -

Kadeethum T, Nick H, Richardson CN, Ballarin F, Lee S. Enriched Galerkin Discretization for Modelling Flow in Fractured Porous Media using Mixed-Dimensional Approach. 2019. Abstract from FEniCS'19, Washington DC, United States.