Computation, Volume 4, Issue 2 (June 2016) – 7 articles

We propose an online adaptive local-global POD-DEIM model reduction method for flows in heterogeneous porous media. The main idea of the proposed method is to use local online indicators to decide on the global update, which is performed via reduced cost local multiscale basis functions. This unique local-global online combination allows (1) developing local indicators that are used for both local and global updates (2) computing global online modes via local multiscale basis functions. The multiscale basis functions consist of offline and some online local basis functions. The approach used for constructing a global reduced system is based on Proper Orthogonal Decomposition (POD) Galerkin projection. The nonlinearities are approximated by the Discrete Empirical Interpolation Method (DEIM). The online adaption is performed by incorporating new data, which become available at the online stage. Once the criterion for updates is satisfied, we adapt the reduced system online by changing the POD subspace and the DEIM approximation of the nonlinear functions. The main contribution of the paper is that the criterion for adaption and the construction of the global online modes are based on local error indicators and local multiscale basis function which can be cheaply computed. Since the adaption is performed infrequently, the new methodology does not add significant computational overhead associated with when and how to adapt the reduced basis. Our approach is particularly useful for situations where it is desired to solve the reduced system for inputs or controls that result in a solution outside the span of the snapshots generated in the offline stage. Our method also offers an alternative of constructing a robust reduced system even if a potential initial poor choice of snapshots is used. Applications to single-phase and two-phase flow problems demonstrate the efficiency of our method. Full article

In the cathode side of a polymer electrolyte fuel cell (PEFC), a micro porous layer (MPL) added between the catalyst layer (CL) and the gas diffusion layer (GDL) plays an important role in water management. In this work, by using both quasi-static and dynamic pore-network models, water and vapor transport in the MPL and GDL has been investigated. We illustrated how the MPL improved water management in the cathode. Furthermore, it was found that dynamic liquid water transport in the GDL was very sensitive to the built-up thermal gradient along the through-plane direction. Thus, we may control water vapor condensation only along GDL-land interfaces by properly adjusting the GDL thermal conductivity. Our numerical results can provide guidelines for optimizing GDL pore structures for good water management. Full article

Benchmark calculations provide a large amount of information that can be very useful in assessing the performance of density functional approximations, and for choosing the one to use. In order to condense the information some indicators are provided. However, these indicators might be insufficient and a more careful analysis is needed, as shown by some examples from an existing data set for cubic crystals. Full article

We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals. Full article

In this paper, the Diffusion Limited Cluster Aggregation (DLCA) method is employed to reconstruct the three-dimensional network of silica aerogel. Then, simulation of nitrogen adsorption at 77 K in silica aerogel is conducted by the Grand Canonical Monte Carlo (GCMC) method. To reduce the computational cost and guarantee accuracy, a continuous-discrete hybrid potential model, as well as an adsorbed layer thickness estimation method, is employed. Four different structures are generated to investigate impacts of specific surface area and porosity on adsorptive capacity. Good agreement with experimental results is found over a wide range of relative pressures, which proves the validity of the model. Specific surface area and porosity mainly affect nitrogen uptake under low pressure and high pressure, respectively. Full article

We model the behavior of an ideal liquid junction, across a porous and possibly charged medium between two ion-containing solutions, by means of the Nernst–Planck equation for the stationary state, in conditions of local electroneutrality. An analytical solution of the equation was found long ago by Planck for the uncharged junction with only ions of valences +1 and −1. Other analytical results, which have later been obtained also for more general situations, seem impractical for performing calculations. In this paper, we obtain analytical solutions for systems with up to three valence classes, which can be applied to perform numerical calculations in a straightforward way. Our method provides a much larger amount of information on the behavior of the system than the well-known Henderson’s approximation. At the same time, it is more simple and reliable, and much less demanding in terms of computational effort, than the nowadays commonly employed numerical methods, typically based on discrete integration and trial-and-error numerical inversions. We present some examples of practical applications of our results. We study in particular the uphill transport (i.e., the transport from the lower-concentration to the higher-concentration region) of a divalent cation in a liquid junction containing also other univalent anions and cations. Full article

Finite-temperature density functional theory (DFT) has become of topical interest, partly due to the increasing ability to create novel states of warm-correlated matter (WCM).Warm-dense matter (WDM), ultra-fast matter (UFM), and high-energy density matter (HEDM) may all be regarded as subclasses of WCM. Strong electron-electron, ion-ion and electron-ion correlation effects and partial degeneracies are found in these systems where the electron temperature T_e is comparable to the electron Fermi energy E_F. Thus, many electrons are in continuum states which are partially occupied. The ion subsystem may be solid, liquid or plasma, with many states of ionization with ionic charge Z_j. Quasi-equilibria with the ion temperature T_i ≠ T_e are common. The ion subsystem in WCM can no longer be treated as a passive “external potential”, as is customary in T = 0 DFT dominated by solid-state theory or quantum chemistry. Many basic questions arise in trying to implement DFT for WCM. Hohenberg-Kohn-Mermin theory can be adapted for treating these systems if suitable finite-T exchange-correlation (XC) functionals can be constructed. They are functionals of both the one-body electron density ne and the one-body ion densities ρj. Here, j counts many species of nuclei or charge states. A method of approximately but accurately mapping the quantum electrons to a classical Coulomb gas enables one to treat electron-ion systems entirely classically at any temperature and arbitrary spin polarization, using exchange-correlation effects calculated in situ, directly from the pair-distribution functions. This eliminates the need for any XC-functionals. This classical map has been used to calculate the equation of state of WDM systems, and construct a finite-T XC functional that is found to be in close agreement with recent quantum path-integral simulation data. In this review, current developments and concerns in finite-T DFT, especially in the context of non-relativistic warm-dense matter and ultra-fast matter will be presented. Full article