Convolution-based particle tracking method for transient flow

Abstract

A convolution-based particle tracking (CBPT) method was recently developed for calculating solute concentrations (Robinson et al., Comput Geosci 14(4): 779–792, 2010). This method is highly efficient but limited to steady-state flow conditions. Here, we present an extension of this method to transient flow conditions. This extension requires a single-particle tracking process model run, with a pulse of particles introduced at a sequence of times for each source location. The number and interval of particle releases depends upon the transients in the flow. Numerical convolution of particle paths obtained at each release time and location with a time-varying source term is performed to yield the shape of the plume. Many factors controlling transport such as variation in source terms, radioactive decay, and in some cases linear processes such as sorption and diffusion into dead-end pores can be simulated in the convolution step for Monte Carlo-based analysis of transport uncertainty. We demonstrate the efficiency of the transient CBPT method, by showing that it requires fewer particles than traditional random walk particle tracking methods to achieve the same levels of accuracy, especially as the source term increases in duration or is uncertain. Since flow calculations under transient conditions are often very expensive, this is a computationally efficient yet accurate method.