When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

Linear solvers for reservoir simulation applications are the objective of this review.
Specifically, we focus on techniques for Fully Implicit (FI) solution methods, in which the set …

Many subsurface engineering applications involve tight-coupling between fluid flow, solid
deformation, fracturing, and similar processes. To better understand the complex interplay of …

We present a family of multi-stage preconditioners for coupled thermal-compositional-
reactive reservoir simulation problems. The most common preconditioner used in industrial …

Accurate black oil reservoir simulation is important for the understanding of underground
resources in hydrology and petroleum reservoir engineering. The success of fast prediction …

For both isothermal and thermal petroleum reservoir simulation, the constrained pressure
residual (CPR) method is the industry-standard preconditioner. This method is a two-stage …

Abstract The space fractional Cahn–Hilliard phase-field model is more adequate and
accurate in the description of the formation and phase change mechanism than the classical …

Porous media processes involve various physical phenomena such as mechanical
deformation, transport, and fluid flow. Accurate simulations must capture the strong …

With the incremental applications of Newton–Krylov methods for solving large sparse
nonlinear systems of equations, the design of robust and scalable linear preconditioners …

Massively parallel simulation of multiphase flows in porous media is challenging due to the
highly nonlinear governing equations with the complexity of various modeling features and …