Multigrid reduction preconditioning framework for coupled processes in porous and fractured media

TL;DR

This paper introduces a flexible multigrid reduction framework for preconditioning large, ill-conditioned linear systems in coupled porous media simulations, enabling scalable and efficient solutions across various complex subsurface processes.

Contribution

The paper presents a novel algebraic preconditioning framework based on multigrid reduction that is adaptable to diverse physics and discretizations in coupled porous media problems.

Findings

The framework produces scalable preconditioners for complex flow and fracture simulations.

Numerical examples demonstrate efficiency and scalability on field-scale problems.

Applicable to multiple discretization schemes and coupled processes.

Abstract

Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design efficient and safe operations, numerical simulations are widely used. Given the relatively long time-scales of interest, fully-implicit time-stepping schemes are often necessary to avoid time-step stability restrictions. A major computational bottleneck for these methods, however, is the linear solver. These systems are extremely large and ill-conditioned. Because of the wide range of processes and couplings that may be involved--e.g. formation and propagation of fractures, deformation of the solid porous medium, viscous flow of one or more fluids in the pores and fractures, complicated well sources and sinks, etc.--it is difficult to develop general-purpose but scalable linear solver frameworks. This challenge is further aggravated by the range of different discretization schemes that may be adopted, which have a direct impact on the linear system structure. To address this obstacle, we describe a flexible framework based on multigrid reduction that can produce purely algebraic preconditioners for a wide spectrum of relevant physics and discretizations. We demonstrate its broad applicability by constructing scalable preconditioners for several problems, notably: a hybrid discretization of single-phase flow, compositional multiphase flow with complex wells, and hydraulic fracturing simulations. Extension to other systems can be handled quite naturally. We demonstrate the efficiency and scalability of the resulting solvers through numerical examples of difficult, field-scale problems.