An Efficient ELLAM Implementation for Modeling Solute Transport in Fractured Porous Media

The goal of this study is to introduce an adaptation of the Eulerian-Lagrangian localized adjoint method (ELLAM) for the simulation of mass transport in fractured porous media, and to evaluate the performance of ELLAM in such a case. The fractures are represented explicitly using the discrete fracture model. The velocity field was calculated using the mixed hybrid finite element method. A sound ELLAM implementation is developed to address numerical artifacts (spurious oscillations and numerical dispersion) arising from the presence of fractures. The efficiency of the developed ELLAM implementation was further improved by taking advantage of the parallel computing on shared memory architecture for the tasks related to particles tracking and linear system resolving. The performance of ELLAM was tested by comparing its results with the Eulerian discontinuous Galerkin method based on several benchmark problems dealing with different fracture configurations. The results highlight the robustness and accuracy of ELLAM, as it allows the use of large time steps, and overcomes the Courant-Friedrichs-Lewy (CFL) restriction. The outcome also shows that ELLAM is more efficient when fracture density is increased.