Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system - Inria EPFL Access content directly
Preprints, Working Papers, ... Year : 2022

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

Abstract

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.
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Dates and versions

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

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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⟩
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