A Comparison of Linear Solvers for Resolving Flow in Three‐Dimensional Discrete Fracture Networks. Issue 4 (13th April 2022)

• Record Type: Journal Article
• Authors: Greer, S. Y.; Hyman, J. D.; O'Malley, D.
• Is Part Of: Water resources research. Volume 58:Issue 4(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-04-13
• Subjects: fracture flow -- discrete fracture network -- numerical methods; Hydrology -- Periodicals; 333.91
• DOI: 10.1029/2021WR031188
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: 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