A general purpose parallel Fortran code for grid projected concentration reconstruction from multidimensional particle distributions

Abstract

Particle-based transport models are widely used for simulating the movement of pollutants in environmental systems. Unlike grid-based methods, particles naturally address advective transport without numerical dispersion. However, these models require concentration reconstruction from the discrete particle information. This is computationally demanding in multidimensional problems, posing a challenge for field-scale models requiring frequent reconstruction. Grid Projected Kernel Density Estimation (GPKDE) is a cell-averaged reconstruction with improvements in computational performance compared to classical KDE. Currently, no programs implementing this method are readily integrated into particle simulators, compatible with three-dimensional domains, and particles with unequal weights. This article introduces a Fortran code for general-purpose GPKDE, with modular functionalities facilitating the integration into external software. The program implements locally adaptive kernel bandwidth selection and alternatives for the reconstruction from particles with non-uniform weights. The code is parallelized with the OpenMP library. Numerical test cases demonstrate the program’s applicability and scalability of the parallel implementation.