Comparison of Two- and Three-field Formulation Discretizations for Flow and Solid Deformation in Heterogeneous Porous Media

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Abstract

We illustrate the advantages and disadvantages among two- and three-field formulations that are used to mimic the flow and solid deformation in heterogeneous porous media. Local mass conservation, flux approximation, average permeability alteration at each time step, and degrees of freedom (DOF) are utilized to evaluate each method. Our result presents that four out of six methods provide the local mass conservative while three out of those four methods produce approximately the same flux approximation and permeability alteration. Three-field formulation methods generally require a smaller time step to converge for solving the system of nonlinear equations. Besides, they have more DOF than that of the two-field formulation because they have one more primary variable, i.e. fluid velocity. The two-field formulation that is a combination of continuous and enriched Galerkin function space enjoys all the benefits while requires the least DOF among the methods that preserve local mass conservation property.
Original languageEnglish
Title of host publicationProceedings of 20th Annual Conference of the International Association for Mathematical Geosciences
Number of pages5
Publication date2019
Publication statusPublished - 2019
Event20th Annual Conference of the International Association for Mathematical Geosciences - Penn Stater Hotel, State College, United States
Duration: 10 Aug 201916 Aug 2019
https://www.iamgconferences.org/iamg2019/

Conference

Conference20th Annual Conference of the International Association for Mathematical Geosciences
LocationPenn Stater Hotel
CountryUnited States
CityState College
Period10/08/201916/08/2019
Internet address

Cite this

Kadeethum, T., Nick, H., & Lee, S. (2019). Comparison of Two- and Three-field Formulation Discretizations for Flow and Solid Deformation in Heterogeneous Porous Media. In Proceedings of 20th Annual Conference of the International Association for Mathematical Geosciences
Kadeethum, Teeratorn ; Nick, Hamid ; Lee, S. / Comparison of Two- and Three-field Formulation Discretizations for Flow and Solid Deformation in Heterogeneous Porous Media. Proceedings of 20th Annual Conference of the International Association for Mathematical Geosciences. 2019.
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Kadeethum, T, Nick, H & Lee, S 2019, Comparison of Two- and Three-field Formulation Discretizations for Flow and Solid Deformation in Heterogeneous Porous Media. in Proceedings of 20th Annual Conference of the International Association for Mathematical Geosciences. 20th Annual Conference of the International Association for Mathematical Geosciences, State College, United States, 10/08/2019.

Comparison of Two- and Three-field Formulation Discretizations for Flow and Solid Deformation in Heterogeneous Porous Media. / Kadeethum, Teeratorn; Nick, Hamid; Lee, S.

Proceedings of 20th Annual Conference of the International Association for Mathematical Geosciences. 2019.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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AB - We illustrate the advantages and disadvantages among two- and three-field formulations that are used to mimic the flow and solid deformation in heterogeneous porous media. Local mass conservation, flux approximation, average permeability alteration at each time step, and degrees of freedom (DOF) are utilized to evaluate each method. Our result presents that four out of six methods provide the local mass conservative while three out of those four methods produce approximately the same flux approximation and permeability alteration. Three-field formulation methods generally require a smaller time step to converge for solving the system of nonlinear equations. Besides, they have more DOF than that of the two-field formulation because they have one more primary variable, i.e. fluid velocity. The two-field formulation that is a combination of continuous and enriched Galerkin function space enjoys all the benefits while requires the least DOF among the methods that preserve local mass conservation property.

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Kadeethum T, Nick H, Lee S. Comparison of Two- and Three-field Formulation Discretizations for Flow and Solid Deformation in Heterogeneous Porous Media. In Proceedings of 20th Annual Conference of the International Association for Mathematical Geosciences. 2019