Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system

Résumé

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. This approach is then used for the simulation of the cross-diffusion system using an implicit finite volume scheme.
Fichier principal
Vignette du fichier
0Paper.pdf (802.32 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03441986 , version 1 (22-11-2021)
hal-03441986 , version 2 (04-04-2022)

Identifiants

Citer

Jad Dabaghi, Virginie Ehrlacher, Christoph Strössner. Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system. 2022. ⟨hal-03441986v2⟩
65 Consultations
61 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More