Physics-based preconditioners for flow in fractured porous media

Abstract

Discrete fracture models are an attractive alternative to upscaled models for flow in fractured media, as they provide a more accurate representation of the flow characteristics. A major challenge in discrete fracture simulation is to overcome the large computational cost associated with resolving the individual fractures in large-scale simulations. In this work, two characteristics of the fractured porous media are utilized to construct efficient preconditioners for the discretized flow equations. First, the preconditioners are tailored to the fracture geometry and presumed flow properties so that the dominant features are well represented there. This assures good scalability of the preconditioners in terms of problem size and permeability contrast. For fracture dominated problems, numerical examples show that such geometric preconditioners are comparable or preferable when compared to state-of-the-art algebraic multigrid preconditioners. The robustness of the physics-based preconditioner for less favorable fracture conditions is further demonstrated by a systematic degradation of the fracture hierarchy. Second, the preconditioners are physics preserving in the sense that conservative fluxes can be computed even for an inexact pressure solutions. This facilitates a scheme where accuracy in the linear solver can be traded for efficiency by terminating the iterative solvers based on error estimates, and without sacrificing basic physical modeling principles. With the combination of these two properties a novel preconditioner is obtained which bridges the gap between multiscale approximations and iterative linear solvers.