Mixed-Dimensional Auxiliary Space Preconditioners

Budiša, Ana; Boon, Wietse M.; Hu, Xiaozhe

doi:10.48550/arxiv.1910.04704

Cited by 2 publications

(1 citation statement)

References 27 publications

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“…The study exposed the relative strengths and weaknesses between the participating methods, both in terms of accuracy and computational cost. After the publication of the results, these benchmark cases have been widely applied by the scientific community in testing numerical methods and new simulation tools [3,4,5,6,7,8,9,10,11].…”

Section: Introductionmentioning

confidence: 99%

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

Berre,

Boon,

Flemisch

et al. 2020

Preprint

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Flow in fractured porous media occurs in the earth's subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, we present a portfolio of four benchmark cases for single-phase flow in three-dimensional fractured porous media. The cases are specifically designed to test the methods' capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases.

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Section: Introductionmentioning

confidence: 99%

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

Berre,

Boon,

Flemisch

et al. 2020

Preprint

View full text Add to dashboard Cite

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Block Preconditioners for Mixed-dimensional Discretization of Flow in Fractured Porous Media

Budiša

2019

Preprint

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In this paper, we are interested in an efficient numerical method for the mixed-dimensional approach to modeling single-phase flow in fractured porous media. The model introduces fractures and their intersections as lower-dimensional structures, and the mortar variable is used for flow coupling between the matrix and fractures. We consider a stable mixed finite element discretization of the problem, which results in a parameter-dependent linear system. For this, we develop block preconditioners based on the well-posedness of the discretization choice. The preconditioned iterative method demonstrates robustness with regards to discretization and physical parameters. The analytical results are verified on several examples of fracture network configurations, and notable results in reduction of number of iterations and computational time are obtained.Keywords porous medium ¨fracture flow ¨mixed finite element ¨algebraic multigrid method ¨iterative method ¨preconditioning Mathematics Subject Classification (2010) 65F08, 65F10, 65N30 IntroductionFracture flow has become a case of intense study recently due to many possible subsurface applications, such as CO 2 sequestration or geothermal energy stor-

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Mixed-Dimensional Auxiliary Space Preconditioners

Cited by 2 publications

References 27 publications

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

Block Preconditioners for Mixed-dimensional Discretization of Flow in Fractured Porous Media

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