2016/12/23 by Andreas Nold, Benjamin D. Goddard, Peter Yatsyshin +2
Computer Science · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Bounded function #Collocation (remote sensing) #Collocation method #Computer science #Density functional theory #Exponential function #Gaussian quadrature #Integral equation #Material Dynamics and Properties #Mathematical analysis #Mathematics #Nyström method #Phase Equilibria and Thermodynamics #Physics #Quadrature (astronomy) #Quantum mechanics #Statistical physics #cs.CE #van der Waals force
paper · pdf · doi:10.1016/j.jcp.2016.12.023
openalex publication_date 2016/12/23 · arxiv created 2017/01/22 · arxiv updated 2017/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze 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 specialized 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.