A parallel block preconditioner for large-scale poroelasticity with highly heterogeneous material parameters

Abstract

Large-scale simulations of coupled flow in deformable porous media require iterative methods for solving the systems of linear algebraic equations. Construction of efficient iterative methods is particularly challenging in problems with large jumps in material properties, which is often the case in realistic geological applications, such as basin evolution at regional scales. The success of iterative methods for such problems depends strongly on finding effective preconditioners with good parallel scaling properties, which is the topic of the present paper. We present a parallel preconditioner for Biot's equations of coupled elasticity and fluid flow in porous media. The preconditioner is based on an approximation of the exact inverse of the two-bytwo block system arising from a finite element discretisation. The approximation relies on a highly scalable approximation of the global Schur complement of the coefficient matrix, combined with generally available state-of-the-art multilevel preconditioners for the individual blocks. This preconditioner is shown to be robust on problems with highly heterogeneous material parameters. We investigate the weak and strong parallel scaling of this preconditioner on up to 512 processors and demonstrate its ability on a realistic basin-scale problem in poroelasticity with over eight million tetrahedral elements.

Resolving hydromechanical coupling in two and three dimensions: spontaneous channelling of porous fluids owing to decompaction weakening

“…A number of numerical studies (e.g. Phillips & Wheeler 2008;Haga et al 2012;Wheeler et al 2014, and references therein), have explored linear poro-elastic coupling. At higher stress levels or temeprature, rock deformation deviates significantly from a linear elastic rheology.…”

Numerical Solution of Plate Poroelasticity Problems

“…To solve such system of equations we need to use special computational algorithms (Gaspar et al 2007;Axelsson et al 2013;Haga et al 2012). Therefore, much attention is given to developing algorithms on the basis of splitting schemes with respect to physical processes (Armero and Simo 1992;Jha and Juanes 2007;Kim 2010;Mikelić and Wheeler 2012), when we sequentially solve the equations…”

Preconditioners for multiphase poromechanics with strong capillarity

“…For single‐phase poromechanics, numerous effective preconditioning strategies have been developed, given the widespread use of this model in various applications 66 . Many of these preconditioners exploit a block‐wise factorization to break the coupled problem into simpler‐to‐solve sub‐problems 67–74 . For multiphase poromechanics, on the other hand, solvers to date have mostly relied on sequential‐implicit approaches, in which the mechanical and fluid flow portions of the problem are solved separately and then iterated to obtain the coupled solution 75–78 .…”