Block preconditioners for mixed-dimensional discretization of flow in fractured porous media

Budiša, Ana; Hu, Xiaozhe

doi:10.1007/s10596-020-09984-z

Cited by 17 publications

(11 citation statements)

References 29 publications

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“…Thus, if the linear system is to be solved by iterative methods, traditional preconditioners cannot be expected to perform well, and specialized methods may be preferable. Preconditioners for mixed-dimensional problems are an immature research field, see however [66,67] for examples on how PorePy can be combined with dedicated solvers for mixeddimensional problems.…”

Section: Solvers and Visualizationmentioning

confidence: 99%

PorePy: an open-source software for simulation of multiphysics processes in fractured porous media

et al. 2020

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Development of models and dedicated numerical methods for dynamics in fractured rocks is an active research field, with research moving towards increasingly advanced process couplings and complex fracture networks. The inclusion of coupled processes in simulation models is challenged by the high aspect ratio of the fractures, the complex geometry of fracture networks, and the crucial impact of processes that completely change characteristics on the fracture-rock interface. This paper provides a general discussion of design principles for introducing fractures in simulators, and defines a framework for integrated modeling, discretization, and computer implementation. The framework is implemented in the open-source simulation software PorePy, which can serve as a flexible prototyping tool for multiphysics problems in fractured rocks. Based on a representation of the fractures and their intersections as lower-dimensional objects, we discuss data structures for mixed-dimensional grids, formulation of multiphysics problems, and discretizations that utilize existing software. We further present a Python implementation of these concepts in the PorePy open-source software tool, which is aimed at coupled simulation of flow and transport in three-dimensional fractured reservoirs as well as deformation of fractures and the reservoir in general. We present validation by benchmarks for flow, poroelasticity, and fracture deformation in porous media. The flexibility of the framework is then illustrated by simulations of non-linearly coupled flow and transport and of injection-driven deformation of fractures. All results can be reproduced by openly available simulation scripts.

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Section: Solvers and Visualizationmentioning

confidence: 99%

PorePy: an open-source software for simulation of multiphysics processes in fractured porous media

et al. 2020

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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 ( Arrarás et al, 2019;Budisa and Hu, 2019;Köppel et al, 2019a;2019b;Odsaeter et al, 2019;Schädle et al, 2019 ).…”

Section: Introductionmentioning

confidence: 99%

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

Berre

Boon

Flemisch

et al. 2021

Advances in Water Resources

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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, four benchmark cases for single-phase flow in three-dimensional fractured porous media are presented. 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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“…15) where c 1,\frakq , c 1,\frakp , c 2,\frakq , and c 2,\frakp are positive constants independent of discretization and physical parameters. Following [13,27] and using Theorem 6.2 and (6.12), the condition number of \scrM D \scrA can be directly estimated as \kappa (\scrM D \scrA ) \leq \beta c 2 \gamma c 1 for c 2 = max\{ c 2,\frakq , c 2,\frakp \} and c 1 = min\{ c 1,\frakq , c 1,\frakp \} . Again, if \beta , \gamma , c 1 , and c 2 are independent of the discretization and physical parameters, then \scrM D is a robust preconditioner as well.…”

Section: Block Preconditioners Based On Auxiliary Space Preconditioningmentioning

confidence: 99%

“…Several approaches have recently been proposed in the context of preconditioners for fracture flow problems, in both an equidimensional setting [31] and mixeddimensional formulations [6,8,13]. Similar to [13], we design robust block preconditioners based on the well-posedness of the discrete PDEs using the framework developed in [26,27]. In this work, on the other hand, the mixed-dimensional nodal auxiliary space preconditioners are proposed to invert one of the diagonal blocks.…”

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confidence: 99%

Mixed-Dimensional Auxiliary Space Preconditioners

Budiša¹,

Boon²,

Hu³

2020

SIAM J. Sci. Comput.

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MIXED-DIMENSIONAL AUXILIARY SPACE PRECONDITIONERS \astANA BUDI \v SA \dagger , WIETSE M. BOON \ddagger , AND XIAOZHE HU \S \bfA \bfb \bfs \bft \bfr \bfa \bfc \bft . This work introduces nodal auxiliary space preconditioners for discretizations of mixed-dimensional partial differential equations. We first consider the continuous setting and generalize the regular decomposition to this setting. With the use of conforming mixed finite element spaces, we then expand these results to the discrete case and obtain a decomposition in terms of nodal Lagrange elements. In turn, nodal preconditioners are proposed analogous to the auxiliary space preconditioners of Hiptmair and Xu [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509. Numerical experiments show the performance of this preconditioner in the context of flow in fractured porous media.\bfK \bfe \bfy \bfw \bfo \bfr \bfd \bfs . finite element, mixed-dimensional, iterative method, auxiliary space preconditioning, algebraic multigrid method, fracture flow \bfA \bfM \bfS \bfs \bfu \bfb \bfj \bfe \bfc \bft \bfc \bfl \bfa \bfs \bfs \bfi fi\bfc \bfa \bft \bfi \bfo \bfn \bfs . 65F08, 65N30, 65N55 \bfD \bfO \bfI .

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Block preconditioners for mixed-dimensional discretization of flow in fractured porous media

Cited by 17 publications

References 29 publications

PorePy: an open-source software for simulation of multiphysics processes in fractured porous media

PorePy: an open-source software for simulation of multiphysics processes in fractured porous media

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

Mixed-Dimensional Auxiliary Space Preconditioners

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