Implementation Of Periodic Boundary Conditions Research Articles

Numerical study of the effect of a thin wire on the thermohydraulic performance in a plate fin-and-tube heat exchanger

A numerical study on the effect of a wire on the thermohydraulic performance in a plate-and-tube heat exchanger is performed with the Reynolds Averaged Navier-Stokes Equations approach. The heat exchanger is represented by a small finned tube bank with the implementation of periodic boundary conditions and symmetry conditions. The simulation models the turbulence with the Shear-Stress Transport model (SST k-ω). A benchmark case (without thin wire) is validated with PIV measurements of the horseshoe vortex and semi-empirical correlations for heat transfer. Then, twenty-four simulations are conducted at different dimensionless distances (1.0, 1.2, and 1.4) and angles (0, 15, 30, and 45°) of a thin wire. Predictions show that vortical structures around the thin wire contribute to an increase in thermohydraulic performance if the recirculation zones caused by thin wire do not affect the airflow patterns generated by finned tubes. However, the thermohydraulic performance decreases if airflow patterns are affected by the thin wire. Therefore, thin wire located at a dimensionless distance of 1.2 and angle of 15° generates a 5–6 % profit on the thermohydraulic performance with a pressure drop up to 73 Pa for Re = 2100.

On the realization of periodic boundary conditions for hexagonal unit cells

In the context of homogenization of micro-heterogeneous materials, the choice of the Representative Volume Element (RV E) plays a crucial role. For periodic microstructures, an RV E is an underlying unit cell with periodic boundary conditions. Nevertheless, the question of the implementation of periodic boundary conditions may arise here; for example, some of the applications of periodic boundary conditions in the literature for hexagonal cells are incorrect or they are not given in detail. In this paper, we analyze periodic boundary conditions for two-dimensional hexagonal unit cells. Periodic boundary conditions are characterized by the periodic fluctuations in the displacement fields and anti-periodic traction vectors at associated points of the boundary of the unit cell. From comparative calculations with an ensemble of unit cells, it is evident that the natural choice for vanishing fluctuations is to be set on the midpoints of the six perimeter lines of the cell. The partially applied choice of vanishing fluctuations in the six corner points of the outer edge of the unit cell leads to wrong results. The boundary conditions proposed here are analyzed on the basis of representative examples and compared to the results with the incorrect boundary conditions.

A computational method for determining the linear elastic properties of 2D aperiodic lattice structures

This paper develops a framework for determining the linear elastic properties of non-periodic lattice structures. An element-based material assignment methodology is implemented that facilitates the generation and analyses of arbitrary patterns on a structured mesh. An adapted numerical homogenization strategy features the inclusion of a homogenized region in the neighbourhood of the domain boundary that validates the implementation of periodic boundary conditions for an arbitrary finite patch of a periodic or non-periodic lattice structure. To demonstrate the method, the linear elastic properties of an aperiodic lattice pattern based on the Penrose (P3) pattern is evaluated. Such a structure exhibits order without translational symmetry and consequently lacks a repeating unit cell. The isotropic performance of the aperiodic lattice structure is investigated and compared to that of the well-known square periodic lattice. The framework opens the door to the investigation and analyses of other novel cellular structures which are not based on a repeating unit cell. Additive manufacturing facilitates the physical realization of such lattice structures, presenting them as viable alternatives to conventional periodic structures in the aerospace and bio-engineering industries.

Periodic DFTB for Supported Clusters: Implementation and Application on Benzene Dimers Deposited on Graphene

The interest for properties of clusters deposited on surfaces has grown in recent years. In this framework, the Density Functional based Tight Binding (DFTB) method appears as a promising tool due to its ability to treat extended systems at the quantum level with a low computational cost. We report the implementation of periodic boundary conditions for DFTB within the deMonNano code with k-points formalism and corrections for intermolecular interactions. The quality of DFTB results is evaluated by comparison with dispersion-corrected DFT calculations. Optimized lattice properties for a graphene sheet and graphite bulk are in agreement with reference data. The deposition of both benzene monomer and dimers on graphene are investigated and the observed trends are similar at the DFT and DFTB levels. Moreover, interaction energies are of similar orders of magnitude for these two levels of calculation. This study has evidenced the high stability of a structure made of two benzene molecules deposited close to each other on the graphene sheet. This work demonstrates the ability of the new implementation to investigate surface-deposited molecular clusters properties.

Finite-Difference Time-Domain Modeling of Periodic Structures: A review of constant wave vector techniques

This article reviews state-of-the-art periodic boundary conditions (PBCs) in finite difference time-domain (FDTD) simulations that operate by enforcing constant wave vector components. The mathematical principles and 3D FDTD implementation details are systematically outlined. Techniques for extracting scattering parameters, Brillouin diagrams, and attenuation constants are presented along with the array scanning method (ASM) used to model the interaction of nonperiodic sources with periodic structures. Through these techniques, the robustness, utility, and efficiency of PBCs are demonstrated and a unified view of the various approaches to the FDTD implementation of PBCs is presented.

Implementation of periodic boundary conditions for loading of mechanical metamaterials and other complex geometric microstructures using finite element analysis

The implementation of periodic boundary conditions (PBCs) is one of the most important and difficult steps in the computational analysis of structures and materials. This is especially true in cases such as mechanical metamaterials which typically possess intricate geometries and designs which makes finding and implementing the correct PBCs a difficult challenge. In this work, we analyze one of the most common PBCs implementation technique, as well as implement and validate an alternative generic method which is suitable to simulate any possible 2D microstructural geometry with a quadrilateral unit cell regardless of symmetry and mode of deformation. A detailed schematic of how both these methods can be employed to study 3D systems is also presented.

Analytic gradient for the QM/MM-Ewald method using charges derived from the electrostatic potential: Theory, implementation, and application to ab initio molecular dynamics simulation of the aqueous electron.

We report an implementation of periodic boundary conditions for mixed quantum mechanics/molecular mechanics (QM/MM) simulations, in which atomic partial charges are used to represent periodic images of the QM region. These charges are incorporated into the Fock matrix in a manner that preserves the variational nature of the self-consistent field procedure, and their interactions with the MM charges are summed using the conventional Ewald technique. To ensure that the procedure is stable in arbitrary basis sets, the atomic charges are derived by least-squares fit to the electrostatic potential generated by the QM region. We formulate and implement analytic energy gradients for the QM/MM-Ewald method and demonstrate that stable molecular dynamics simulations are thereby obtained. As a proof-of-concept application, we perform QM/MM simulations of a hydrated electron in bulk liquid water at the level of Hartree-Fock theory plus empirical dispersion. These simulations demonstrate that the "cavity model" of the aqueous electron, in which the spin density of the anionic defect is localized within an excluded volume in the liquid, is stable at room temperature on a time scale of at least several picoseconds. These results validate cavity-forming pseudopotential models of e-(aq) that have previously been derived from static-exchange Hartree-Fock calculations, and cast doubt upon whether non-cavity-forming pseudopotentials are faithful to the underlying Hartree-Fock calculation from which they were obtained.

Efficient implementation of periodic boundary conditions in Monte Carlo simulation.

Determination of the shortest distances between particles is one of the most time-consuming parts of molecular simulation by the Monte Carlo method. In this work, we demonstrate that the use of signed-integer storage of coordinates in a scaled box allows one to skip multiple conditional statements in realization of periodic boundary conditions in cubic and rectangular boxes, which, in turn, increases the performance. Performance of the improved procedure was tested in NVT Monte Carlo simulations for liquid krypton and water. © 2018 Wiley Periodicals, Inc.

A continuum-atomistic multi-scale technique for nonlinear behavior of nano-materials

In this paper, a hierarchical RVE-based continuum-atomistic multi-scale procedure is developed to model the nonlinear behavior of nano-materials. The atomistic RVE is accomplished in consonance with the underlying atomistic structure, and the inter-scale consistency principals, i.e. kinematic and energetic consistency principals, are exploited. To ensure the kinematic compatibility between the fine- and coarse-scales, the implementation of periodic boundary conditions is elucidated for the fully atomistic method. The material properties of coarse-scale are modeled with the nonlinear finite element method, in which the stress tensor and tangent modulus are computed using the Hill-Mandel principal through the atomistic RVE. In order to clearly represent the mechanical behavior of the fine-scale, the stress-strain curves of the atomistic RVE undergoing distinct type of deformation modes are delineated. These results are then assessed to obtain the proper fine-scale parameters for the multi-scale analysis. Finally, several numerical examples are solved to illustrate the capability of the proposed computational algorithm.

A sharp-interface Immersed Boundary Method to simulate convective and conjugate heat transfer through highly complex periodic porous structures

Immersed boundary method (IBM) based CFD code has helped considerably in avoiding the tedious grid generation process in fluid flows involving complex geometries. In this work, we have developed an IBM framework to simulate flow, convective heat transfer as-well-as conjugate heat transfer through a highly complex random porous structure. In this framework, we can incorporate any complex solid body as a triangulated surface mesh and an accurate algorithm is proposed to identify solid cells and fluid cells. Moreover, a detailed implementation of periodic boundary condition for velocity and temperature is presented. Detailed code verification process is performed to demonstrate that the method is second-order accurate for both the velocity and temperature fields for all the boundary conditions considered. The developed scheme is shown to be applicable for convective and conjugate heat transfer through highly complex computer-generated realistic open-cell solid foams in a periodic Cartesian domain.

Introduction of periodic boundary conditions into UNRES force field.

In this article, implementation of periodic boundary conditions (PBC) into physics-based coarse-grained UNited RESidue (UNRES) force field is presented, which replaces droplet-like restraints previously used. Droplet-like restraints are necessary to keep multichain systems together and prevent them from dissolving to infinitely low concentration. As an alternative for droplet-like restrains cuboid PBCs with imaging of the molecules were introduced. Owing to this modification, artificial forces which arose from restraints keeping a droplet together were eliminated what leads to more realistic trajectories. Due to computational reasons cutoff and smoothing functions were introduced on the long range interactions. The UNRES force field with PBC was tested by performing microcanonical simulations. Moreover, to asses the behavior of the thermostat in PBCs Langevin and Berendsen thermostats were studied. The influence of PBCs on association pattern was compared with droplet-like restraints on the ββα hetero tetramer 1 protein system.

Meso-scale analysis of angle-ply laminates

In this paper, a meso-scale repeated unit cell model for a general [θ]n angle-ply laminate is developed and the implementation of periodic boundary conditions in a finite element analysis for this 3-D model is presented. A nonlinear viscoelastic constitutive model and a post-damage constitutive model based on the concept of a smeared crack are also incorporated in the finite element analysis. The stress-strain response and the damage initiation and propagation for different values of θ are predicted.

Finite-Element Modeling of Evanescent Modes in the Stopband of Periodic Structures

A novel implementation of periodic boundary conditions in the finite-element method is presented that is applicable to complex eigenmode analysis of the electromagnetic waves in infinite periodic media. A weighted residual finite-element (FE) model is employed to obtain the attenuation constant of evanescent/complex modes within bandgaps by analyzing only one unit cell of the structure. Plots of the imaginary and the real parts of the propagation constants versus frequency are shown which confirms the capability of the developed FE code in capturing complex modes.

Modeling the Thermal Conductivity and Phonon Transport in Nanoparticle Composites Using Monte Carlo Simulation

Abstract This paper presents a Monte Carlo simulation scheme to study the phonon transport and the thermal conductivity of nanocomposites. Special attention has been paid to the implementation of periodic boundary condition in Monte Carlo simulation. The scheme is applied to study the thermal conductivity of silicon germanium (Si–Ge) nanocomposites, which are of great interest for high-efficiency thermoelectric material development. The Monte Carlo simulation was first validated by successfully reproducing the results of (two-dimensional) nanowire composites using the deterministic solution of the phonon Boltzmann transport equation reported earlier and the experimental thermal conductivity of bulk germanium, and then the validated simulation method was used to study (three-dimensional) nanoparticle composites, where Si nanoparticles are embedded in Ge host. The size effects of phonon transport in nanoparticle composites were studied, and the results show that the thermal conductivity of nanoparticle composites can be lower than that of the minimum alloy value, which is of great interest to thermoelectric energy conversion. It was also found that randomly distributed nanopaticles in nanocomposites rendered the thermal conductivity values close to that of periodic aligned patterns. We show that interfacial area per unit volume is a useful parameter to correlate the size effect of thermal conductivity in nanocomposites. The key for the thermal conductivity reduction is to have a high interface density where nanoparticle composites can have a much higher interface density than the simple 1D stacks, such as superlattices. Thus, nanocomposites further benefit the enhancement of thermoelectric performance in terms of thermal conductivity reduction. The thermal conductivity values calculated by this work qualitatively agrees with a recent experimental measurement of Si–Ge nanocomposites.

Periodic Boundary Conditions for Dislocation Dynamics Simulations in Three Dimensions

This article presents an implementation of periodic boundary conditions (PBC) for Dislocation Dynamics (DD) simulations in three dimensions (3D). We discuss fundamental aspects of PBC development, including preservation of translational invariance and line connectivity, the choice of initial configurations compatible with PBC and a consistent treatment of image stress. On the practical side, our approach reduces to manageable proportions the computational burden of updating the long-range elastic interactions among dislocation segments. The timing data confirms feasibility and practicality of PBC for large-scale DD simulations in 3D.

Periodic Boundary Conditions for Dislocation Dynamics Simulations in Three Dimensions

AbstractThis article presents an implementation of periodic boundary conditions (PBC) for Dislocation Dynamics (DD) simulations in three dimensions (3D). We discuss fundamental aspects of PBC development, including preservation of translational invariance and line connectivity, the choice of initial configurations compatible with PBC and a consistent treatment of image stress. On the practical side, our approach reduces to manageable proportions the computational burden of updating the long-range elastic interactions among dislocation segments. The timing data confirms feasibility and practicality of PBC for large-scale DD simulations in 3D.

Infinite phased-array analysis using FDTD periodic boundary conditions-pulse scanning in oblique directions

Unit cell analysis of infinite phased-arrays in the finite difference time domain (FDTD) is performed by implementation of periodic boundary conditions. The technique allows for pulse excitation and oblique scan directions in both the cardinal and intercardinal planes. To our knowledge, this is the first paper presenting FDTD computations for intercardinal pulse scanning in oblique directions. The ordinary Yee lattice is used, which makes the algorithm easy to incorporate in an already existing FDTD code. Nonperiodic boundaries are truncated by Berenger's (see J. Comput. Phys., vol.127, p.363-79, 1996) perfectly matched layer (PML). Active impedance of an infinite dipole array is calculated with the new method and validation is performed via the element-by-element approach, i.e., by a conventional FDTD simulation of a corresponding large finite array. Excellent agreement is found and the technique has been numerically stable in all cases analyzed.

Time-domain analysis of periodic structures at oblique incidence: orthogonal and nonorthogonal FDTD implementations

A novel implementation of periodic boundary conditions incorporated into the finite-difference time-domain (FDTD) technique in both orthogonal and nonorthogonal grids is presented in this paper. The method applied is a field-splitting approach to the discretization of the Floquet-transformed Maxwell equations. As a result, the computational burden is reduced and the stability criterion is relaxed. The results of the two methods are compared to experimental data.

Investigation of the losses in the stator duct spacers of large AC motors using the A-ψ 3-D eddy current formulation

This paper describes how the A-/spl psi/ formulation may be applied to determine the losses in the stator duct spacers of large AC motors. The model is described in terms of its geometry and boundary conditions. The novel aspects of the application of the formulation to this problem are explained. These include the modelling of fixed currents sources (the stator windings), the location of the necessary cut surfaces and the determination of their magnetic scalar potential differences, and the implementation of periodic boundary conditions for vector variables. Results are presented showing how the duct spacer losses vary with load, and with the relative permeability of the spacer material. The effects of modelling iron nonlinearity, of both the spacer and the steel laminations, are also illustrated.