The particle support volume is crucial for simulating reactive transport with Lagrangian methods as it dictates the interaction among particles. Assuming that it is constant in space, the particle support volume can be selected by means of kernel density estimation theory, an approach that has been shown to provide accurate estimates in simple setups. However, the particle support volume should intuitively vary with the particle position and evolve with time so as to mimic the local behavior of the solute plume. In this paper, we present a new approach to select a locally optimal particle support volume in reactive transport simulations. We consider that each particle has a different support volume that can locally adapt its shape and size with time based on the nearby particle distribution. By introducing a new optimality criterion, closed-form expressions of the particle support volume are presented under certain assumptions. In advection-dominated transport, we propose to orient the support volume along the local velocities. Numerical simulations of solute transport in a randomly heterogeneous porous medium demonstrate that the new approach can substantially increase accuracy with a more rapid convergence to the true solution with the number of particles. The error reduction seen in local approaches is particularly important in regions with extreme (high and low) density of particles. The method is shown to be computationally efficient, displaying better results than traditional histogram or global kernel methods for the same computational effort.

Peer Reviewed