In this work, we review a set of consistent discretizations for second-order elliptic equations, and compare and contrast them with respect to accuracy, monotonicity, and factors affecting their computational cost (degrees of freedom, sparsity, and condition numbers). Our comparisons include the...

We present a robust and flexible sequential solution approach in which the flow equation is solved on the original grid, whereas the transport equations are solved with a new dynamic coarsening method that adapts the grid resolution locally to reduce the number of cells as much as possible. The...

The Monte Carlo (MC) method is an appealing candidate for uncertainty quantification in reservoir simulation for three reasons: (i) It is the preferred approach for systematic reduction in variance for cases with high-dimensional uncertainty with a strongly nonlinear effect (robustness); (ii) it is...

Thermal energy from medium to high-enthalpy aquifers is an appealing energy resource: it is renewable, always on, and, at least in principle, available anywhere on the planet. Moreover, and perhaps equally important, aquifers are excellent candidates for flexible large-scale energy storage. This is...

The fully implicit method is the most commonly used approach to solve black-oil problems in reservoir simulation. The method requires repeated linearization of large nonlinear systems and produces ill-conditioned linear systems. We present a strategy to reduce computational time that relies on two...