Particle Density Estimation with Grid-Projected Adaptive Kernels

Abstract

The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) models of solute transport in fluids. In random walk particle tracking (RWPT) simulations, particle density is directly linked to solute concentrations, which is normally the main variable of interest, not just for visualization and post-processing of the results, but also for the computation of non-linear processes, such as chemical reactions. Previous works have shown the superiority of kernel density estimation (KDE) over other methods such as binning, in terms of its ability to accurately estimate the "true" particle density relying on a limited amount of information. Here, we develop a grid-projected KDE methodology to determine particle densities by applying kernel smoothing on a pilot binning; this may be seen as a "hybrid" approach between binning and KDE. The kernel bandwidth is optimized locally. Through simple implementation examples, we elucidate several appealing aspects of the proposed approach, including its computational efficiency and the possibility to account for typical boundary conditions, which would otherwise be cumbersome in conventional KDE.

References in corpus (4)

• Kernel density estimation via diffusion
• Accelerating and parallelizing Lagrangian simulations of mixing-limited reactive transport
• A second order scheme for a Robin boundary condition in random walk algorithms
• Numerical Equivalence Between SPH and Probabilistic Mass Transfer Methods for Lagrangian Simulation of Dispersion

Cited by in corpus (3)

• A Mass-transfer Particle-tracking Method for Simulating Transport with Discontinuous Diffusion Coefficients
• Reactive Particle-tracking Solutions to a Benchmark Problem on Heavy Metal Cycling in Lake Sediments
• Global random walk solvers for reactive transport and biodegradation processes in heterogeneous porous media