  Modeling flow through porous media with multiple pore-networks has now become
an active area of research due to recent technological endeavors like
geological carbon sequestration and recovery of hydrocarbons from tight rock
formations. Herein, we consider the double porosity/permeability (DPP) model,
which describes the flow of a single-phase incompressible fluid through a
porous medium exhibiting two dominant pore-networks with a possibility of mass
transfer across them. We present a stable mixed discontinuous Galerkin (DG)
formulation for the DPP model. The formulation enjoys several attractive
features. These include: (i) Equal-order interpolation for all the field
variables (which is computationally the most convenient) is stable under the
proposed formulation. (ii) The stabilization terms are residual-based, and the
stabilization parameters do not contain any mesh-dependent parameters. (iii)
The formulation is theoretically shown to be consistent, stable, and hence
convergent. (iv) The formulation supports non-conforming discretizations and
distorted meshes. (v) The DG formulation has improved element-wise (local) mass
balance compared to the corresponding continuous formulation. (vi) The proposed
formulation can capture physical instabilities in coupled flow and transport
problems under the DPP model.
