Projection functions for particle‐grid methods

Abstract

AbstractRandom walk particle methods (RWPM) can be used in operator splitting schemes to simulate reactive solute transport in porous media. Projection functions are used to transfer particle location and mass information to concentrations at selected spatial points. Because of the stochastic nature of RWPM, concentration estimates made from particle distributions include a “noisy” error component. In some cases of reactive or density‐dependent flows, this type of error may be propagated forward in time. It can be reduced by using larger numbers of particles or by using different projection functions. The effects of using different projection functions or numbers of particles in different flow regimes or dimensions are explored using concentration solutions for a set of one‐, two‐, and three‐dimensional nonreactive test problems. Resulting solutions are compared with analytic results and classical random walk error estimates. A piecewise linear projection function provides a reasonable improvement in accuracy over the more convenient box methods at a modest increase in cost. The support of the projection functions should be O(Δx) to avoid excessive smearing. Multidimensional projection functions may be advantageously formed by products of different one‐dimensional projection functions.