A coupled finite element–global random walk approach to advection-dominated transport in porous media with random hydraulic conductivity

Solute transport through heterogeneous porous media considered in environmental and industrial problems is often characterized by high Péclet numbers. In this paper we develop a new numerical approach to advection-dominated transport consisting of coupling an accurate mass-conservative mixed finite element method (MFEM), used to solve Darcy flows, with a particle method, stable and free of numerical diffusion, for non-reactive transport simulations. The latter is the efficient global random walk (GRW) algorithm, which performs the simultaneous tracking of arbitrarily large collections of particles on regular lattices at computational costs comparable to those of single-trajectory simulations using traditional particle tracking (PT). MFEM saturated flow solutions are computed for spatially heterogeneous hydraulic conductivities parameterized as samples of random fields. The coupling is achieved by projecting the velocity field from the MFEM basis onto the regular GRW lattice. Preliminary results show that MFEM–GRW is tens of times faster than the full MFEM flow and transport simulation.