  Simulation of multiphase poromechanics involves solving a multi-physics
problem in which multiphase flow and transport are tightly coupled with the
porous medium deformation. To capture this dynamic interplay, fully implicit
methods, also known as monolithic approaches, are usually preferred. The main
bottleneck of a monolithic approach is that it requires solution of large
linear systems that result from the discretization and linearization of the
governing balance equations. Because such systems are non-symmetric,
indefinite, and highly ill-conditioned, preconditioning is critical for fast
convergence. Recently, most efforts in designing efficient preconditioners for
multiphase poromechanics have been dominated by physics-based strategies.
Current state-of-the-art "black-box" solvers such as algebraic multigrid (AMG)
are ineffective because they cannot effectively capture the strong coupling
between the mechanics and the flow sub-problems, as well as the coupling
inherent in the multiphase flow and transport process. In this work, we develop
an algebraic framework based on multigrid reduction (MGR) that is suited for
tightly coupled systems of PDEs. Using this framework, the decoupling between
the equations is done algebraically through defining appropriate interpolation
and restriction operators. One can then employ existing solvers for each of the
decoupled blocks or design a new solver based on knowledge of the physics. We
demonstrate the applicability of our framework when used as a "black-box"
solver for multiphase poromechanics. We show that the framework is flexible to
accommodate a wide range of scenarios, as well as efficient and scalable for
large problems.
