Hybrid sub-gridding ADE–FDTD method of modeling periodic metallic nanoparticle arrays

In this paper, a modified sub-gridding scheme that hybridizes the conventional finite-difference time-domain（FDTD）method and the unconditionally stable locally one-dimensional（LOD） FDTD is developed for analyzing the periodic metallic nanoparticle arrays. The dispersion of the metal, caused by the evanescent wave propagating along the metal-dielectric interface, is expressed by the Drude model and solved with a generalized auxiliary differential equation（ADE） technique.In the sub-gridding scheme, the ADE–FDTD is applied to the global coarse grids while the ADE–LOD–FDTD is applied to the local fine grids. The time step sizes in the fine-grid region and coarse-grid region can be synchronized, and thus obviating the temporal interpolation of the fields in the time-marching process. Numerical examples about extraordinary optical transmission through the periodic metallic nanoparticle array are provided to show the accuracy and efficiency of the proposed method.

Sub-gridding FDTD Algorithm for 3D Numerical Analysis of EM Scattering and Radiation Problems

The finite-difference time-domain(FDTD)method is used effectively to solve electromagnetic(EM)scattering and radiation problems using a 3D sub-gridding algorithm.For accuracy and stability of the FDTD method,the computational domain of EM problems with locally fine structures or electrically small objects is discretized with finer grids.This sub-gridding algorithm for different regions of the computational domain was implemented to increase the accuracy and reduce the computational time and memory requirements compared to those of the traditional FDTD method.In the sub-gridding algorithm,the FDTD computational domain is divided into separate regions:coarse grid and fine grid regions.Since the cell sizes and time steps are different in the coarse and fine grid regions,interpolations in both time and space are used to evaluate the electric and magnetic fields on the boundaries between different regions.The accuracy of the developed 3D sub-gridding algorithm has been verified for radiation and scattering problems,including multiple fine grid regions.Excellent performance is obtained even for higher and different contrast ratios in fine grid regions.

Impacts of the Thermal Effects of Sub-grid Orography on the Heavy Rainfall Events Along the Yangtze River Valley in 1991

A P - σ regional climate model using a parameterization scheme to account for the thermal effects of the sub-grid scale orography was used to simulate the three heavy rainfall events that occurred within the Yangtze River Valley during the mei-yu period of 1991. The simulation results showed that by considering the sub-grid scale topography scheme, one can significantly improve the performance of the model for simulating the rainfall distribution and intensity during these three heavy rainfall events, most especially the second and third. It was also discovered that the rainfall was mainly due to convective precipitation. The comparison between experiments, either with and without the sub-grid scale topography scheme, showed that the model using the scheme reproduced the convergence intensity and distribution at the 850 hPa level and the ascending motion and moisture convergence center located at 500 hPa over the Yangtze River valley. However, some deviations still exist in the simulation of the atmospheric moisture content, the convergence distribution and the moisture transportation route, which mainly result in lower simulated precipitation levels. Further analysis of the simulation results demonstrated that the sub-grid topography scheme modified the distribution of the surface energy budget components, especially at the south and southwest edges of the Tibetan Plateau, leading to the development and eastward propagation of the negative geopotential height difference and positive temperature-lapse rate difference at 700 hPa, which possibly led to an improved precipitation simulation over eastern China.

The impact of heterogeneity of land surface roughness length on estimation of turbulent flux in model

Based on preliminary theoretical analysis and numerical experiment, it is found that land surface heterogeneity plays an important role in the models turbulent flux calculation. In nearly neutral atmosphere conditions, variation coefficient of sub-scale roughness length, cell-average roughness, and reference height are main factors affecting the calculation of grid turbulent fluxes. The first factor has a determinant role on calculation deviation. The relative error generated by roughness heterogeneity could be more than 40% in some cases in certain areas （e.g., in vegetation-climate transition belt）. Selecting a specific reference height may improve the calculation of turbulent flux. In stable or unstable atmosphere conditions, with sensible heat flux as an example, analysis shows that the discrepancy is correlated to the sub-grid distributions of mean wind velocity, potential temperature gradient between land surface and reference levels, and atmosphere stability near surface layer caused by the heterogeneity of land surface roughness. The calculation of turbulent flux is the most sensitive to stability in the above three factors. The above analysis shows that it is necessary to make a further consideration for the calculation deviation of the turbulent fluxes brought from land surface heterogeneity in the present numerical models.

Large-Eddy Simulations of turbulent flows with lattice Boltzmann dynamics and dynamical system sub-grid models

In this paper, two sub-grid scale (SGS) models are introduced into the Lattice Boltzmann Method (LBM), i.e., the dynamics SGS model and the dynamical system SGS model, and applied to numerically solving three-dimensional high Re turbulent cavity flows. Results are compared with those obtained from the Smagorinsky model and direct numerical simulation for the same cases. It is shown that the method with LBM dynamics SGS model has advantages of fast computation speed, suitable to simulate high Re turbulent flows. In addition, it can capture detailed fine structures of turbulent flow fields. The method with LBM dynamical system SGS model dose not contain any adjustable parameters, and can be used in simulations of various complicated turbulent flows to obtain correct information of sub-grid flow field, such as the backscatter of energy transportation between large and small scales. A new average method of eliminating the inherent unphysical oscillation of LBM is also given in the paper.

Some notes on numerical simulation of the turbulent cavitating flow with a dynamic cubic nonlinear sub-grid scale model in OpenFOAM

The accuracy of large eddy simulation(LES)is highly dependent on the performance of sub-grid scale(SGS)model.In the present paper,a dynamic cubic nonlinear sub-grid scale model(DCNM)proposed by Huang et al.is implemented for the simulation of unsteady cavitating flow around a 3-D Clark-Y hydrofoil in OpenFOAM.Its performance in predicting the evolution of cloud cavitation is discussed in detail.The simulation with a linear model,the dynamic Smagorinsky model(DSM),is also conducted as a comparison.The results with DCNM show a better agreement with the available experimental observation.The comparison between DCNM and DSM further suggests that the DCNM is able to predict the backscatter more precisely,which is an important feature in LES.The characteristics of DCNM is analyzed to account for its advantages in the prediction of unsteady cloud cavitation as well.The results reveal that it is the nonlinear terms of DCNM that makes DCNM capture sub-grid scale vortices better and more suitable for studying the transient behaviors of cloud cavitation than DSM.

Numerical investigation of the effect of sub-grid scale eddies on the dispersed particles by LES/FDF model

An LES/FDF model was developed by the authors to investigate the SGS effect on the particle motion in the gas-particle two-phase plane wake flow.The simulation results of dispersion rate for different particles were compared with the results without using the FDF model.It was shown that the large eddy structure is the dominant factor influencing the particle diffu-sion in space for small particles(small Stokes-number particles),but for intermediate or large diameter particles,the influence of the sub-grid scale eddies on the dispersion rate is in the same order as that of the large eddies.The sub-grid scale eddies increase the particle dispersion rate in most time,but sometimes they decrease the dispersion rate.The sub-grid scale particle dispersion rate is decided not only by the intensity of sub-grid scale eddies and the Stokes number of the particles,but also by the large eddy structure of the flow field.For the particles in isotropic turbulence,the dispersion rate decreases as the particle diameter increases.

Wall shear-stress extraction by an optical flow algorithm with a sub-grid formulation

In this study,we developed a novel optical-flow algorithm for determining the wall shear-stress on the surface of objects.The algorithm solves the thin-oil-film equation using a numerical scheme that recovers local features neglected by smoothing filters.A variational formulation with a smoothness constraint was applied to extract the global shear-stress fields.The algorithm was then applied to scalar images generated using direct numerical simulation(DNS)method,which revealed that the errors were smaller than those of conventional methods.The application of the proposed algorithm to recover the wall shear-stress on a low-aspect-ratio wing and on an axisymmetric boattail model taken as examples in this study showed a strong potential for analysing shear-stress fields.Compared to the methods used in previous studies,proposed method reveals more local features of separation line and singular points on object surface.

A Sub-Grid Structure Enhanced Discontinuous Galerkin Method for Multiscale Diffusion and Convection-Diffusion Problems

In this paper,we present an efficient computational methodology for diffusion and convection-diffusion problems in highly heterogeneous media as well as convection-dominated diffusion problem.It is well known that the numerical computation for these problems requires a significant amount of computermemory and time.Nevertheless,the solutions to these problems typically contain a coarse component,which is usually the quantity of interest and can be represented with a small number of degrees of freedom.There are many methods that aim at the computation of the coarse component without resolving the full details of the solution.Our proposed method falls into the framework of interior penalty discontinuous Galerkin method,which is proved to be an effective and accurate class of methods for numerical solutions of partial differential equations.A distinctive feature of our method is that the solution space contains two components,namely a coarse space that gives a polynomial approximation to the coarse component in the traditional way and a multiscale space which contains sub-grid structures of the solution and is essential to the computation of the coarse component.In addition,stability of the method is proved.The numerical results indicate that the method can accurately capture the coarse behavior of the solution for problems in highly heterogeneous media as well as boundary and internal layers for convection-dominated problems.

LARGE EDDY SIMULATION OF THERMALLY-STRATIFIED TURBULENT CHANNEL FLOW WITH TEMPERATURE OSCILLATION ON THE BOTTOM WALL

Thermally-stratified shear turbulent channel flow with temperatureoscillation on the bottom wall of the channel was investigated with the Large Eddy Simulation (LES)approach coupled with dynamic Sub-Grid-Scale (SGS) models. The effect of temperature oscillation onthe turbulent channel flow behavior was examined. The phase-averaged velocities and temperature, andflow structures at different Richardson numbers and periods of the oscillation was analyzed.

LARGE-EDDY AND DETACHED-EDDY SIMULATIONS OF THE SEPARATED FLOW AROUND A CIRCULAR CYLINDER

The separated turbulent flow around a circular cylinder is investigated using Large-Eddy Simulation （LES）, Detached-Eddy Simulation （DES, or hybrid RANS/LES methods）, and Unsteady Reynolds-Averaged Navier-Stokes （URANS）. The purpose of this study is to examine some typical simulation approaches for the prediction of complex separated turbulent flow and to clarify the capability of applying these approaches to a typical case of the separated turbulent flow around a circular cylinder. Several turbulence models, i.e. dynamic Sub-grid Scale （SGS） model in LES, the DES-based Spalart-Allmaras （S-A） and κ-ω Shear-Stress- Transport （SST） models in DES, and the S-A and SST models in URANS, are used in the calculations. Some typical results, e.g., the mean pressure and drag coefficients, velocity profiles, Strouhal number, and Reynolds stresses, are obtained and compared with previous computational and experimental data. Based on our extensive calculations, we assess the capability and performance of these simulation approaches coupled with the relevant turbulence models to predict the separated turbulent flow.

LARGE EDDY SIMULATION OF PARTICLE TRANSPORT IN FULLY DEVELOPED VERTICAL TURBULENT CHANNEL FLOW

Fully developed vertical turbulent channel flow with particle transport wasinvestigated by use of Large Eddy Simulation (LES) approach coupled with dynamic the Sub-Grid Scale(SGS) model. It was assumed that the motion of each particle is followed in a Lagrangian frame ofreference driven by the forces exerted by fluid motion and gravity under the condition of one-waycoupling. The goal of this study is to investigate the effectiveness of the LES technique forpredicting particle transport in turbulent flow and the behavior of particle-laden turbulent channelflow for three kinds of particles at different Stokes numbers. To depict the behavior ofparticle-laden turbulent channel flow, statistical quantities including particle fluctuation andfluid-particle velocity correlation, and visualization of the particle number density field wereanalyzed.

LARGE EDDY SIMULATION (LES) OF TURBULENT FLOW BY FINITE DIFFERENCE METHOD

A Large Eddy Simulation (LES) technique was applied to solve the turbulentchannel flow for Re_τ = 150 . Three types of turbulence models are employed, such as theSmagorinsky model, the Dynamic Sub-Grid Scale(SGS) model and the Generalized Normal Stress (GNS)model. The simulated data in time series for the LES were averaged in both time and space to carryout the statistical analysis. Results of LES were compared with that of a DNS. As an application, aLES technique was used for 2D body in order to check the validation by investigating the turbulentvortical motion around the afterbody with a slant angle.

A Mathematical Analysis of Scale Similarity

Scale similarity is found in many natural phenomena in the universe,from fluid dynamics to astrophysics.In large eddy simulations of turbulent flows,some sub-grid scale(SGS)models are based on scale similarity.The earliest scale similarity SGS model was developed by Bardina et al.,which produced SGS stresses with good correlation to the true stresses.In the present study,we perform a mathematical analysis of scale similarity.The analysis has revealed that the ratio of the resolved stress to the SGS stress is g2,where g is the ratio of the second filter width to the first filter width,under the assumption of small filter width.The implications of this analysis are discussed in the context of large eddy simulation.