  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-condi\-tioned linear
systems. We present a strategy to reduce computational time that relies on two
key ideas: (\textit{i}) a sequential formulation that decouples flow and
transport into separate subproblems, and (\textit{ii}) a highly efficient
Gauss--Seidel solver for the transport problems. This solver uses intercell
fluxes to reorder the grid cells according to their upstream neighbors, and
groups cells that are mutually dependent because of counter-current flow into
local clusters. The cells and local clusters can then be solved in sequence,
starting from the inflow and moving gradually downstream, since each new cell
or local cluster will only depend on upstream neighbors that have already been
computed. Altogether, this gives optimal localization and control of the
nonlinear solution process.
  This method has been successfully applied to real-field problems using the
standard first-order finite volume discretization. Here, we extend the idea to
first-order dG methods on fully unstructured grids. We also demonstrate proof
of concept for the reordering idea by applying it to the full simulation model
of the Norne oil field, using a prototype variant of the open-source OPM Flow
simulator.
