A multidimensional streamline-based method to simulate reactive solute transport in heterogeneous porous media

We present a new streamline-based numerical method for simulating reactive solute transport in porous media. The key innovation of the method is that both longitudinal and transverse dispersion are incorporated accurately without numerical dispersion. Dispersion is approximated in a flow-oriented grid using a combination of a one-dimensional finite difference scheme and a meshless approximation. In contrast to previous hybrid alternatives to incorporate dispersion in streamline-based simulations, the proposed scheme does not require a grid and, hence, it does not introduce numerical dispersion. In addition, the proposed scheme eliminates numerical oscillations and negative concentration values even when the dispersion tensor includes the off-diagonal coefficients and the flow field is non-uniform. We demonstrate that for a set of two- and three-dimensional benchmark problems, the new proposed streamline-based formulation compares favorably to two state of the art finite volume and hybrid Eulerian–Lagrangian solvers.