Volume 73, 2023CEMRACS 2021 - Data Assimilation and Reduced Modeling for High Dimensional Problems
|Page(s)||173 - 186|
|Published online||30 August 2023|
Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system
Ecole des Ponts ParisTech, Marne-la-Vallée, France
2 INRIA Paris, France
3 Institute of Mathematics, EPF Lausanne, Switzerland
Cross-diffusion systems arise as hydrodynamic limits of lattice multi-species interacting particle models. The objective of this work is to provide a numerical scheme for the simulation of the cross-diffusion system identified in [J. Quastel, Comm. Pure Appl. Math., 45 (1992), pp. 623–679]. To simulate this system, it is necessary to provide an approximation of the so-called self-diffusion coefficient matrix of the tagged particle process. Classical algorithms for the computation of this matrix are based on the estimation of the long-time limit of the average mean square displacement of the particle. In this work, as an alternative, we propose a novel approach for computing the self-diffusion coefficient using deterministic low-rank approximation techniques, as the minimum of a high-dimensional optimization problem. The computed self-diffusion coefficient is then used for the simulation of the cross-diffusion system using an implicit finite volume scheme.
© EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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