Solving density driven flow problems with efficient spatial discretizations and higher-order time integration methods

Modelling density driven flow problems requires an excessive computational time and/or heavy equipments due to the non-linear coupling between flow and transport equations. In this work, we develop a robust numerical model with efficient advanced approximations for both spatial and temporal discretizations in order to reduce the excessive computational requirement while maintaining accuracy. The spatial discretization is based upon the lumped formulation of the mixed finite element method for the flow equation, the discontinuous Galerkin method for advection and the multipoint flux approximation method for dispersion. The method of lines (MOL) is used to allow higher-order temporal discretization of the coupled flow-transport system. The developed model adapts in both the order of approximation and time step to provide the necessary accuracy. Standard numerical test cases as well as a laboratory scale experiment with a high viscosity contrast between injected and displaced fluids are simulated to show drawbacks of the standard approach and to highlight the efficiency, accuracy and robustness of the developed model for density driven flow problems.