Discontinuous low order pressure formulation in control volume finite element method for simulating flow and transport in highly heterogeneous porous media

Control volume finite element (CVFE) methods provide flexible framework for modelling flow and transport in complex geological features such as faults and fractures. They combine the finite element method that captures complex flow characteristics with the control volume approach known for its stability and mass conservative properties. The general approach of CVFE methods maps the physical properties of the system onto the element mesh (element-wise properties) while the node centred control volumes span element boundaries. In the presence of abrupt material interfaces between elements which are often encountered in fractured models, the method suffers from non-physical leakage in the saturation solution as the result of control volume discretization used for advancing the transport solution. In this work, we present a discontinuous pressure formulation based on control volume finite element (CVFE) method for modelling coupled flow and transport in highly heterogeneous porous media. We propose the element pair P_(1,DG)-P_(0,DG), a discontinuous first order velocity approximation combined with a discontinuous low order pressure approximation. The approach circumvents the non-physical leakage issue by incorporating a discontinuous, element-based approximation of pressure. Hence, the resultant control volume representation directly maps to the element mesh as well as to the projected physical properties of the system. Due to the low order nature of the formulation, low computational requirement per element and the improved control volume discretization, the presented formulation is proven more robust and accurate than classical CVFE methods in the presence of highly heterogeneous domains.