Modelling variable density flow problems in heterogeneous porous media using the method of lines and advanced spatial discretization methods

Modelling variable density flow problems under heterogeneous porous media conditions requires very long computation time and high performance equipments. In this work, the DASPK solver for temporal resolution is combined with advanced spatial discretization schemes in order to improve the computational efficiency while maintaining accuracy.The spatial discretization is based on a combination of Mixed Finite Element (MFE), Discontinuous Galerkin (DG) and Multi-point Flux Approximation methods (MPFA). The obtained non-linear ODE/DAE system is solved with the Method of Lines (MOL) using the DASPK time solver. DASPK uses the preconditioned Krylov iterative method to solve linear systems arising at each time step.Precise laboratory-scale 2D experiments were conducted in a heterogeneously packed porous medium flow tank and the measured concentration contour lines are used to evaluate the numerical model. Simulations show the high efficiency and accuracy of the code and the sensitivity analysis confirms the density dependence of dispersion.