Coupled nonlinear surface reactions in random walk particle tracking

Abstract

Random walk particle tracking (RWPT) methods employ a Lagrangian discretization of transported scalars into point particles to numerically solve the advection–dispersion equation. Their recognized advantages regarding numerical stability and numerical dispersion make them ideal candidates to tackle reactive transport problems. However, limitations in the classes of boundary conditions that can currently be treated restrict the range of interface processes that can be simulated. Here, we derive and verify a new collision-based approach to implement a broad class of generalized Robin-type boundary conditions, representing the balance between diffusive fluxes and an arbitrary nonlinear function of the transported and surface reactant concentrations. This formulation allows for modeling coupled sets of surface reactions with arbitrary nonlinear kinetics within the classical RWPT framework. The collision-based nature of the proposed technique allows for estimating surface reaction rates based on single-particle collisions with the reactive interface, relying only on a discretization of the boundary as commonly used for collision detection under conservative transport. Thus, the method does not require concentration field reconstructions within the transport domain or multi-particle searches.