Numerical Simulation of Reactive Transport via Particle Tracking (Random Walk)

Amir Paster, School of Mechanical Engineering, Tel Aviv University, Tel Aviv, Israel
Diogo Bolster, Civil & Environmental Engineering And Earth Sciences, University Of Notre Dame, Notre Dame, United States

Reactive transport in a fluid environment can be modeled by the Advection-Reaction-Diffusion-Equation (ADRE). When Peclet number is high, i.e. when the advection term is dominating the diffusion term, modeling the ADRE by a numerical code based on finite differences or finite elements can lead to significant numerical dispersion, i.e. inaccuracy in the results. To avoid this, different numerical approaches,  based on a Lagrangian point of view, were developed. However these approaches were so far unable to handle the case of kinetic bi-molecular reaction A+B->C. In recent years, we developed a particle tracking approach that tackles this case. In essence, the particles represent the mass of the chemical components, and move in space as a result of the advection term; In addition, they perform a random walk that represents the diffusion term. The novel part of our model is the application of the reaction term, which is handled by calculating the co-location probability of close-by particles. This probability, multiplied by the kinetic rate constant of the reaction, dictates whether or not a particle pair will be annihilated in a time step.

The approach has been developed and presented in a series of papers (Paster et al., Water Resources Research, 2013, Paster et al, Journal of Computational Physics, 2014, Paster et al, Physical Review E, 2015, Bolster et al, WRR, 2016). In my talk I will present our most recent results from this on-going research.