Convergence of mass transfer particle tracking schemes for the simulation of advection-diffusion-reaction equations

Stephen Pankavich, Lucas Schauer, Michael J. Schmidt, Nicholas B. Engdahl, Diogo Bolster and David A. Benson

Applied Mathematics and Computation, 2025, vol. 496, issue C

Abstract: Since their introduction [1,2], multi-species mass-transfer particle tracking (or MTPT) algorithms have been used to accurately simulate advective and dispersive transport of solutes, even within systems that feature nonlinear chemical reactions. The MTPT methods were originally derived from a probabilistic or first-principles perspective and have previously lacked a more rigorous derivation arising directly from the underlying advection-diffusion-reaction equation (ADRE). Herein, we provide a fully rigorous derivation of the MTPT method as a Lagrangian approximation of solutions to the ADRE, complete with a description of the error and order of accuracy generated by this approximation. Numerical simulations further detail the fidelity of MTPT methods and display parameter regimes wherein the numerical error is independent of the chosen time step, and thereby dependent only upon the numerical discretization of the spatial domain via the number of particles within a simulation. Finally, different normalizations of the local Green's function are shown to generate similar approximations of the underlying solution for stationary particles.

Keywords: Lagrangian modeling; Convergent numerical method; Particle methods; Mass-transfer particle-tracking; Porous media (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300325000852
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:496:y:2025:i:c:s0096300325000852

DOI: 10.1016/j.amc.2025.129358

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().