Simulating nonlinear surface reactions using particle tracking.


Random walk particle tracking (RWPT) methods employ a Lagrangian discretization of solute plumes into point particles to numerically solve the advection-dispersion equation. Their recognized advantages over more traditional grid-based Eulerian methods regarding numerical stability and numerical dispersion make them ideal candidates to simulate complex reactive fronts in heterogeneous media. However, handling nontrivial boundary conditions is challenging, restricting the range of interface processes that can be simulated. In this talk, I will give a brief introduction to random walk particle tracking and present a new method to model arbitrary coupled sets of nonlinear surface reactions within the classical RWPT framework. These reactions can be represented in an Eulerian framework as generalized Robin boundary conditions, where surface reaction rates equal incoming diffusive fluxes. The new Lagrangian random walk representation is based on single-particle collisions with the reactive interface, from which diffusive fluxes and concentrations at the interface are estimated in order to compute nonlinear reaction rates. Thus, it does not require concentration field reconstructions or multi-particle searches. I discuss the convergence and stability of the method for a coupled set of nonlinear mass-action reactions under pure diffusion, as well as an example application to an advective-diffusive transport problem with nonlinear surface kinetics representing calcite dissolution in a model porous medium.


2022 | UPC - CSIC. Unidad Asociada: Grupo de Hidrología Subterránea