An optimal-transport finite-particle method for driven mass diffusion

Creators: Pandolfi, A.¹; Romero, I.^{2, 3}; Ortiz, Michael⁴

1. Politecnico di Milano
2. Technical University of Madrid
3. IMDEA Materials
4. California Institute of Technology

Abstract

We formulate a finite-particle method of mass transport that accounts for general mixed boundary conditions. The particle method couples a geometrically-exact treatment of advection; Wasserstein gradient-flow dynamics; and a Kullback–Leibler representation of the entropy. General boundary conditions are enforced by introducing an adsorption/depletion layer at the boundary wherein particles are added or removed as dictated by the boundary conditions. We demonstrate the range and scope of the method through a number of examples of application, including absorption of particles into a sphere and flow through pipes of square and circular cross section, with and without occlusions. In all cases, the solution is observed to converge weakly, or in the sense of local averages.

Copyright and License

© 2025 The Authors. Published by Elsevier B.V. This is an open access article distributed under the terms of the Creative Commons CC-BY license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Acknowledgement

AP is grateful for the support of the Italian National Group of Physics-Mathematics (GNFM) of the Italian National Institution of High Mathematics “Francesco Severi” (INDAM). IR acknowledges the support of the Spanish Ministry of Science and Innovation under project PID2021-128812OB-I00. MO gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via project 211504053 - SFB 1060; project 441211072 - SPP 2256; and project 390685813 - GZ 2047/1 - HCM.

Code Availability

The code used for the examples in this article is freely available in the public repository: https://gitlab.com/ignacio.romero/finite-particles

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