Numerical methods for flow in fractured porous media

We present a numerical technique for the simulation of salinity- as well as thermohaline-driven flows in fractured porous media. In this technique, the fractures are represented by low-dimensional manifolds, on which a low-dimensional variant of the PDEs of variable-density flow is formulated. The latter is obtained from the full-dimensional model by the average-along-the-vertical. The discretization of the resulting coupled system of the full- and low-dimensional PDEs is based on a finite-volume method. This requires a special construction of the discretization grid which can be obtained by the algorithm presented in this work. This technique allows to reconstruct in particular the jumps of the solution at the fracture. Its precision is demonstrated in the numerical comparisons with the results obtained in the simulations where the fractures are represented by the full-dimensional subdomains.