Pseudospectral methods for density functional theory in bounded and unbounded domains

JOURNAL OF COMPUTATIONAL PHYSICS

卷:334

Article

Nold, Andreas^1,5  Goddard, Benjamin D.^2,3  Yatsyshin, Peter¹  Savva, Nikos⁴  Kalliadasis, Serafim¹ 

[1] Imperial Coll London, Dept Chem Engn, London SW7 2AZ, England

[2] Univ Edinburgh, Sch Math, Edinburgh EH9 3FD, Midlothian, Scotland

[3] Univ Edinburgh, Maxwell Inst Math Sci, Edinburgh EH9 3FD, Midlothian, Scotland

[4] Cardiff Univ, Sch Math, Cardiff CF24 4AG, S Glam, Wales

[5] Max Planck Inst Brain Res, Theory Neural Dynam, D-60438 Frankfurt, Germany

关键词: Density functional theory;    Pseudospectral methods;   

DOI  :  10.1016/j.jcp.2016.12.023

来源: Elsevier

【 摘 要 】

Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyse fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of interfacial phenomena, as well as problems in adsorption, colloidal science and phase transitions in fluids. Typical DFT equations are highly non-linear, stiff and contain several convolution terms. We propose a novel, efficient pseudo-spectral collocation scheme for computing the non-local terms in real space with the help of a specialised Gauss quadrature. Due to the exponential accuracy of the quadrature and a convenient choice of collocation points near interfaces, we can use grids with a significantly lower number of nodes than most other reported methods. We demonstrate the capabilities of our numerical methodology by studying equilibrium and dynamic two-dimensional test cases with single-and multispecies hard-sphere and hard disc particles modelled with fundamental measure theory, with and without van der Waals attractive forces, in bounded and unbounded physical domains. We show that our results satisfy statistical mechanical sum rules. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free