Accelerate the Electrolyte Perturbed-Chain Statistical Associating Fluid Theory–Density Functional Theory Calculation With the Chebyshev Pseudo-Spectral Collocation Method. Part II. Spherical Geometry and Anderson Mixing

Abstract

To improve the efficiency of electrolyte perturbed-chain statistical associating fluid theory–density functional theory (ePC-SAFT-DFT) calculation of the confined system, in this work, first, the Chebyshev pseudo-spectral collocation method was extended to the spherical pores. Second, it was combined with the Anderson mixing algorithm to accelerate the iterative process. The results show that the Anderson mixing algorithm can reduce the computation time significantly. Finally, based on the accelerated ePC-SAFT-DFT program, a systematic study of the effects of the temperature, pressure, pore size, and pore shape on the CO2 solubilities in the ionic liquids (ILs) confined inside the silica nanopores was conducted. Based on the simulation results, to obtain high CO2 solubilities in the ILs confined in silica, a better option is to use the silica material with a narrow spherical pore, and the IL-anion should be selected specifically considering that it has a more significant impact on the absorption enhancement effect.

Two-Dimensional PC-SAFT-DFT Adsorption Models for Carbon Slit-Shaped Pores with Surface Energetical Heterogeneity and Geometrical Corrugation

“…In order to avoid divergence, 10 steps of Picard iterations were performed at the beginning and then switched to the Anderson mixing procedure. The density profile calculated with the corresponding one-dimension (1D) system (i.e., α in eq equals to 0) is used as the initial guess (1D DFT calculation with the Chebyshev pseudospectral collocation method can be referred to in refs , ). As illustrated in Figure , it takes less than 2 s for 2D PC-SAFT-DFT calculation to get an accurate density profile using the Chebyshev pseudospectral collocation method.…”

“…For the terms of type I, the interpolation region for the weighted density profile should be larger than that for the density profile and a detailed discussion can be referred to our previous studies. 57 The external potential change dramatically near the wall, which implies that more collocation points are required in these regions compared with the middle of the slit. In this work, in the x-direction, the conformal map proposed by Bayliss and Turkel was used to map the Chebyshev collocation points {c k } to domain [0, H'/2]: 66…”

“…In other words, this domain is discretized for interpolating the density profile function. For the terms of type I, the interpolation region for the weighted density profile should be larger than that for the density profile and a detailed discussion can be referred to our previous studies …”

“…Yatsyshin et al , proposed the Chebyshev pseudospectral collocation method for solving the DFT equation; a detailed description of this method can be referred to Nold et al’s work . In the Chebyshev pseudospectral collocation method, the grids can be clustered in the domain where the external potential changes dramatically. − This indicates that the Chebyshev pseudospectral collocation method may be an effective strategy to improve the 2D PC-SAFT-DFT calculation efficiency in modeling confined systems.…”

Analysis of Vapor–Liquid Interfacial Transport Resistivities with DGT-PC-SAFT Based on the General Approach

“…High density of points near the boundaries may necessitate very small time steps in an explicit time-stepping spectral method or make the matrix conditions involved in implicit time-stepping terribly poor. − Furthermore, the low density points in the middle of the domain may lead to the use of more points to resolve the solution, which can be avoided by combining rational interpolants with adaptive grid points . This approach was used to represent the density profile among fluid–solid interfaces in several previous studies − and termed as the Chebyshev spectral collocation method in this work. Considering that the gradient of the density profile is more significant in the middle of the vapor–liquid interface, the Chebyshev spectral collocation method may be a promising scheme for solving the DGT equation.…”