This work presents a space-time adaptive framework for simulating multi-phase flows
through porous media, with specific applications to flows in oil reservoirs. A fully
unstructured discretization of space and time is used instead of a conventional time-
marching approach. For d-dimensional spatial problems, this requires the generation
of (d+1)-dimensional meshes, where time is treated as an additional spatial dimension.
Anisotropic mesh adaptation is performed based on a posteriori error estimation
to reduce the error of a specified output of interest. This work makes use of the
DWR method for error estimation and the MOESS algorithm for metric-based mesh
optimization. A discontinuous Galerkin finite element discretization is used to solve
on simplex meshes with arbitrary anisotropy, and thereby obtain solutions of higher
order accuracy in both space and time. The adaptive framework has been applied to
single-phase and two-phase flow test problems in a one-dimensional reservoir, and the
results were compared to those obtained from a time-marching finite volume method
that is representative of a typical industrial simulator.