Combined finite element - particles discretisation for simulation of transport-dispersion in porous media

Combining finite element together with particle methods provide one of the best compromise for solving transport problem in porous media. Saturated or non-saturated flows are determined by boundary condition and the media permeability. For real terrain, permeability can consist in various almost constant and imbricated zones with complex shapes. Thus, it is of some interest that the boundary between two adjacent zones coincides with a natural mesh interface and that each element is entirely contains in one such zone. Beside this, solving transport equation by means of particle methods offers two distinctive advantages. The method is unconditionally stable when applied to a pure convective equation, and it does not contain any numerical diffusion if the particle trajectories are correctly computed. Therefore the combination of finite elements and particle method appears to be a straightforward application of the principle : ”the right method at the right place”. Although the previous statement provide a consistent basis to build a numerical model, there still remain some options in the choice of the two components themself. To start with, it has long been recognised that the computed flow must satisfied as much as possible the divergence free condition; this can be achieved by selecting a non-conforming or mixed method. Second, there exist many way to design particles methods for the convective part as well as for the dispersion term. For the first one, a so-called streamline method