A Comparison of Linear Solvers for Resolving Flow in Three‐Dimensional Discrete Fracture Networks

We compare various methods for resolving steady flow within three‐dimensional discrete fracture networks, including direct methods, Krylov subspace methods with and without preconditioning, and multi‐grid methods. We compared the performance of the methods based on compute times and scaling of the s...

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Bibliographic Details
Published in:Water resources research 2022-04, Vol.58 (4), p.n/a
Main Authors: Greer, S. Y., Hyman, J. D., O’Malley, D.
Format: Article
Language:English
Subjects:
Apertures
Cholesky factorization
discrete fracture network
Factorization
fracture flow
GEOSCIENCES
Heterogeneity
Methods
Multigrid methods
Networks
Nodes
numerical methods
Permeability
Preconditioning
Scaling
Steady flow
Subspace methods
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Summary:We compare various methods for resolving steady flow within three‐dimensional discrete fracture networks, including direct methods, Krylov subspace methods with and without preconditioning, and multi‐grid methods. We compared the performance of the methods based on compute times and scaling of the solution as a function of the number of grid nodes and log‐variance of the hydraulic aperture. The methods are applied to three test cases: (a) variable density of networks with a truncated power‐law distribution of fracture lengths, (b) a fixed network composed of monodisperse fracture sizes but varied permeability/aperture heterogeneity, (c) and a network based on field site in Nevada, US. We chose these cases to allow us to study the impact of the mesh size and flow properties, as well as to demonstrate our conclusions on a large‐scale, realistic problem (more than 40 million mesh nodes). A direct solution using Cholesky factorization outperformed other methods for every example but was closely followed in performance by some algebraic multigrid (AMG) preconditioned Krylov subspace methods. Among the Krylov methods, conjugate gradients (CG) with an AMG preconditioner performs the best. Generally, Cholesky factorization is recommended, but CG with an AMG preconditioner may be suitable for very large problems beyond 40 million nodes where the entire linear system cannot reside in memory. Key Points Cholesky factorization generally outperforms alternative methods for solving flow equations in discrete fracture networks The conjugate gradient method combined with an algebraic multigrid (AMG) preconditioner performs the best among iterative methods The conjugate gradient method with an AMG preconditioner competes with Cholesky factorization for huge fracture networks
ISSN:0043-1397
1944-7973
DOI:10.1029/2021WR031188