A finite-volume scheme for gradient-flow equations with non-homogeneous diffusion
File(s)
Accepted version
Author(s)
Mendes, Julien
Russo, Antonio
Perez, Sergio P
Kalliadasis, Serafim
Type
Journal Article
Abstract
We develop a first- and second-order finite-volume scheme to solve gradient flow equations with non-homogeneous properties, obtained in the framework of dynamical-density functional theory. The scheme takes advantage of an upwind approach for the space discretization to ensure positivity of the density under a CFL condition and decay of the discrete free energy. Our computational approach is used to study several one- and two-dimensional systems, with a general free-energy functional accounting for external fields and inter-particle potentials, and placed in non-homogeneous thermal baths characterized by anisotropic, space-dependent and time-dependent properties.
Date Issued
2021-05-01
Date Acceptance
2021-02-08
Citation
Computers & Mathematics with Applications, 2021, 89, pp.150-162
ISSN
0898-1221
Publisher
Elsevier BV
Start Page
150
End Page
162
Journal / Book Title
Computers & Mathematics with Applications
Volume
89
Copyright Statement
© 2021 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Commission of the European Communities
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://www.sciencedirect.com/science/article/pii/S0898122121000407?via%3Dihub
Grant Number
247031
EP/L020564/1
EP/L027186/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Non-homogeneous baths
Finite-volume schemes
Dynamical-density functional theory
DENSITY-FUNCTIONAL THEORY
AGGREGATION
MODEL
Numerical & Computational Mathematics
01 Mathematical Sciences
08 Information and Computing Sciences
15 Commerce, Management, Tourism and Services
Publication Status
Published
Date Publish Online
2021-03-20