Simulation Domain Size Research Articles

Marginal turbulent state of viscoelastic fluids: A polymer drag reduction perspective.

The laminar-turbulent (LT) transition of dilute polymer solutions is of great interest not only for the complex transition dynamics itself, but also for its potential link to the maximum drag reduction (MDR) phenomenon. We present an in-depth investigation of the edge state (ES), an asymptotic solution on the LT boundary, in viscoelastic channel flow. For given Re and simulation domain size, mean flow statistics of the ES do not vary with the introduction of polymers, proving that there is a region of turbulent states not susceptible to polymer drag reduction effects. The dynamics of the ES features low-frequency fluctuations and in the longer domains we studied it is nearly periodic with regular bursts of turbulent activities separated by extended quiescent periods. Its flow field is dominated by elongated vortices and streaks, with very weak extensional and rotational flow motions. Polymer stretching is almost exclusively contributed by the mean shear and polymer-turbulence interaction is minimal. Flow structures and the kinematics of the ES match hibernating turbulence, an MDR-like phase intermittently occurring in turbulent dynamics. Its observation now seems to result from recurrent visits to certain parts of the ES. The ES offers explanations for the existence and universality of MDR, the quantitative magnitude of which, however, still remains unsolved.

Impact of domain size and statistical errors in simulations of homogeneous decaying turbulence and the Richtmyer-Meshkov instability

Both experiments and computations are naturally constrained by boundary conditions. In fundamental problems such as homogeneous decaying turbulence (HDT) or shock-induced mixing layers, a size constraint naturally limits the growth of the large scales in the problem, modifying the physics observed. This paper explores through Large Eddy Simulation (LES) the integral properties using computations from 1283 to 10243 for HDT and 1283 to 5123 for the Richtmyer-Meshkov instability (RMI). Kinetic energy decay rates in both cases are shown to be relatively insensitive to the domain size until the spectral peak is at the first wave number. The integral length is significantly more sensitive, showing substantial discrepancies once it is greater than 10% of the domain size. However, the key error is shown to be due to a lack of statistical averaging once the integral length is greater than 5% of the box size, thus appearing earlier than the length scale saturation. This highlights that a single computation at modest grid resolution (≤2563) may not reproduce the correct physics and that at this resolution, numericists need to embrace the practice of using multiple independent realisations to reduce the statistical error, as is the norm for the experimentalist. Finally, an update on the physics of HDT and RMI as predicted through LES computations is presented.

Simulation domain size requirements for elastic response of 3D polycrystalline materials

A fast Fourier transform (FFT) based spectral algorithm is used to compute the full field mechanical response of polycrystalline microstructures. The field distributions in a specific region are used to determine the sensitivity of the method to the number of surrounding grains through quantification of the divergence of the field values from the largest simulation domain, as successively smaller surrounding volumes are included in the simulation. The analysis considers a mapped 3D structure where the location of interest is taken to be a particular pair of surface grains that enclose a small fatigue crack, and synthetically created statistically representative microstructures to further investigate the effect of anisotropy, loading condition, loading direction, and texture. The synthetic structures are generated via DREAM3D and the measured material is a cyclically loaded, Ni-based, low solvus high refractory (LSHR) superalloy that was characterized via 3D high energy x-ray diffraction microscopy (HEDM). Point-wise comparison of distributions in the grain pairs shows that, in order to obtain a Pearson correlation coefficient larger than 99%, the domain must extend to at least the third nearest neighbor. For an elastic FFT calculation, the stress–strain distributions are not sensitive to the shape of the domain. The main result is that convergence can be specified in terms of the number of grains surrounding a region of interest.

Morphology and transport properties of fibrous porous media

The exploration of flow permeability of fibrous media is of great important significance in many industrial applications. Flow permeability strongly depends on the pore-scale structures. In order to explore the morphology of fibrous porous media and furthermore evaluate the transport properties, high-resolution X-ray tomography was employed to study the porous media in this paper. Morphology statistics data of porosity, specific surface area, tortuosity, and pore diameter were obtained. The size of representative volume element (RVE) determined according to geometry statistical deviation was consistent with that estimated with Brickman screening length criterion. The lattice Boltzmann simulation was then performed based on RVE to explore macroscopic transport properties. The transverse flow permeability obtained with Darcy's law at the steady state was consistent with the results in analytical models of layered fiber arrangement. Moreover, the impacts of the size and spatial resolution of simulation domain on the numerical results were discussed. Finally, the linear relationship between permeability and square pore diameter was quantitatively evaluated.

Phase-Field Crystal Model for Fe Connected to MEAM Molecular Dynamics Simulations

A recently developed phase-field crystal (PFC) model incorporates elasticity and plasticity in the microstructural evolution of materials naturally by representing the density field for the crystalline state by periodic functions and by using a constant density for liquid state. PFC is of great interest in nano- and micro-structural modeling of materials because it is a model with atomistic scale details but is applicable to diffusive time scales. However, determining model parameters for specific materials is one of the less developed aspects of PFC modeling. In this article, molecular dynamics (MD) simulations of solid–liquid structures for Fe were performed using the modified embedded-atom method to determine the melting point, latent heat, expansion in melting, density profile, and liquid structure factor. The influence of simulation cell size on the results of MD simulations was also investigated. The melting temperature, density profile, and liquid structure factor were used as inputs to find model parameters required by the PFC model for Fe. The spatial derivative order of the PFC time-evolution equation was reduced from four to two, and the resultant system of partial differential equations was solved numerically using the finite element method. The required simulation domain and element size for the convergence of the PFC simulations were determined, and the expansion in melting, latent heat and solid–liquid surface free energy were calculated. The PFC results were compared with the results of other computational and experimental works in the literature.

Monte Carlo simulation of phonon transport in UO2 single crystals

The Monte Carlo (MC) method is applied to solve the Boltzmann transport equation for phonons in uranium dioxide single crystals, with the objective of understanding thermal transport in this material at the mesoscale. The overall solution scheme tracks the phonon density as it evolves in space and time due to phonon drift and phonon–phonon scattering by normal and Umklapp processes. Unlike most previous works on solving the Boltzmann transport equation for phonons by the MC technique, our scheme for calculating phonon lifetime, based on normal and Umklapp scattering, eliminates the need for using many fitting parameters. Instead, the Grüneisen parameter, which is a well-characterized material property, is the only parameter of the problem. The results elucidate the simulation domain size over which the computed conductivity is size dependent; this helps to determine the minimum domain size required to simulate bulk thermal transport and hence calculate the thermal conductivity. The latter is computed over the temperature range 300–1000 K. The computed conductivity values are in good agreement with the previously published experimental and molecular dynamics simulation results.

Full-Wave Characterization of Rough Terrain Surface Scattering for Forward-Looking Radar Applications

In characterizing ground surface clutter as relevant to forward-looking radar applications, a finite-difference time-domain (FDTD)-based solver is proposed to study dielectric surface scattering at low depression angles. The solver's effectiveness and accuracy are carefully evaluated for one-dimensional surfaces by comparing Monte Carlo scattering results to those from a surface integral equation (SIE) approach for various surface parameters and incidence angles. It is demonstrated that satisfactory results can be attained at near-grazing angles for most surface parameters of interest with a relatively small simulation domain size, independent of the incidence angle. Subsequently, FDTD simulations of two-dimensional terrain surfaces are featured, along with a demonstration of the effects of ground clutter on target imaging generated by the time-reversal technique. By providing a practical full-wave simulation framework for the emulation of forward-looking radar operation and imaging, this study is intended to facilitate ongoing investigations into the detectability of discrete ground targets in the presence of distributed variable ground clutter in the near-grazing regime.

Effects of interface disorder on valley splitting in SiGe/Si/SiGe quantum wells

A sharp potential barrier at the Si/SiGe interface introduces valley splitting (VS), which lifts the 2-fold valley degeneracy in strained SiGe/Si/SiGe quantum wells (QWs). This work examines in detail the effects of Si/SiGe interface disorder on the VS in an atomistic tight binding approach based on statistical sampling. VS is analyzed as a function of electric field, QW thickness, and simulation domain size. Strong electric fields push the electron wavefunctions into the SiGe buffer and introduce significant VS variations from device to device. A Gedankenexperiment with ordered alloys sheds light on the importance of different bonding configurations on VS. We conclude that a single SiGe band offset and effective mass cannot comprehend the complex Si/SiGe interface interactions that dominate VS.

Determination of the decay exponent in mechanically stirred isotropic turbulence

Direct numerical simulation is used to investigate the decay exponent of isotropic homogeneous turbulence over a range of Reynolds numbers sufficient to display both high and low Re number decay behavior. The initial turbulence is generated by the stirring action of the flow past many small randomly placed cubes. Stirring occurs at 1/30th of the simulation domain size so that the low-wavenumber and large scale behavior of the turbulent spectrum is generated by the fluid and is not imposed. It is shown that the decay exponent in the resulting turbulence matches the theoretical predictions for a k2 low-wavenumber spectrum at both high and low Reynolds numbers. The transition from high Reynolds number behavior to low Reynolds number behavior occurs relatively abruptly at a turbulent Reynolds number of around 250 (${\mathop{\rm Re}\nolimits} _\lambda \approx 41$ Re λ≈41).

N-BODY SIMULATION OF PLANETESIMAL FORMATION THROUGH GRAVITATIONAL INSTABILITY AND COAGULATION. II. ACCRETION MODEL

The gravitational instability of a dust layer is one of the scenarios for planetesimal formation. If the density of a dust layer becomes sufficiently high as a result of the sedimentation of dust grains toward the midplane of a protoplanetary disk, the layer becomes gravitationally unstable and spontaneously fragments into planetesimals. Using a shearing box method, we performed local $N$-body simulations of gravitational instability of a dust layer and subsequent coagulation without gas and investigated the basic formation process of planetesimals. In this paper, we adopted the accretion model as a collision model. A gravitationally bound pair of particles is replaced by a single particle with the total mass of the pair. This accretion model enables us to perform long-term and large-scale calculations. We confirmed that the formation process of planetesimals is the same as that in the previous paper with the rubble pile models. The formation process is divided into three stages: the formation of non-axisymmetric structures, the creation of planetesimal seeds, and their collisional growth. We investigated the dependence of the planetesimal mass on the simulation domain size. We found that the mean mass of planetesimals formed in simulations is proportional to $L_y^{3/2}$, where $L_y$ is the size of the computational domain in the direction of rotation. However, the mean mass of planetesimals is independent of $L_x$, where $L_x$ is the size of the computational domain in the radial direction if $L_x$ is sufficiently large. We presented the estimation formula of the planetesimal mass taking into account the simulation domain size.

Multidecadal High-Resolution Hydrologic Modeling of the Arkansas–Red River Basin

Abstract Land surface heterogeneity and its effects on surface processes have been a concern to hydrologists and climate scientists for the past several decades. The contrast between the fine spatial scales at which heterogeneity is significant (1 km and finer) and the coarser scales at which most climate simulations with land surface models are generated (hundreds of kilometers) remains a challenge, especially when incorporating land surface and subsurface lateral fluxes of mass. In this study, long-term observational land surface forcings and derived solar radiation were used to force high-resolution land surface model simulations over the Arkansas–Red River basin in the Southern Great Plains region of the United States. The most unique aspect of these simulations is the fine space (1 km2) and time (hourly) resolutions within the model relative to the total simulation period (51 yr) and domain size (575 000 km2). Runoff simulations were validated at the subbasin scale (600–10 000 km2) and were found to be in good agreement with observed discharge from several unregulated subbasins within the system. A hydroclimatological approach was used to assess simulated annual evapotranspiration for all subbasins. Simulated evapotranspiration values at the subbasin scale agree well with predictions from a simple one-parameter empirical model developed in this study according to Budyko’s concept of “geographical zonality.” The empirical model was further extended to predict runoff and evapotranspiration sensitivity to precipitation variability, and good agreement with computed statistics was also found. Both the empirical model and simulation results demonstrate that precipitation variability was amplified in the simulated runoff. The finescale at which the study is performed allows analysis of various aspects of the hydrologic cycle in the system including general trends in precipitation, runoff, and evapotranspiration, their spatial distribution, and the relationship between precipitation anomalies and runoff and soil water storage anomalies at the subbasin scale.

Effects of Truncation Error of Derivative Approximation for Two-Phase Lattice Boltzmann Method

We verify the accuracy and the truncation errors of approximation to the first derivatives and to Laplacian operator in the lattice Boltzmann method. The truncation errors are calculated by the Taylor series expansion, and the influences are analytically and numerically examined in the simulation of two-phase flow. We propose the 4th-order accurate approximations to derivatives that utilize the property of the tensor unlike the finite difference. The numerical solutions with various approximations agree well with the theoretical ones within the error of 7% in the test of the Laplace's law. Application of the 4th-order accurate approximation scheme to two-phase flow simulation reduces the spurious current around the interface of a stationary droplet about to one-half of the results with the 2nd-order accuracy. The small spurious velocity in the vicinity of the interface of the 4th-order approximation increases the speed of a moving droplet, and distorts the shape of the droplet little. In the simulation of phase separation, the growth rate of the typical domain size calculated with FFT is strongly affected by the truncation error in surface-tension driven regime for short time. It is seen that the 4th-order approximation saturates at 2nd-order accuracy in simulation of a decaying Taylor vortex flow, because the convergence rate of the LBM is 2nd-order in space. It is shown that the approximation method affects the important physical values, such as velocity, moving speed, or domain size in numerical simulations.

Lattice-Boltzmann simulation of grid-generated turbulence

The lattice-Boltzmann method (LBM) is used to carry out a direct numerical simulation (DNS) of grid-generated turbulence with the view to improve comparison between experimental and numerical results on approximate isotropic turbulence. The grid is made up of four by four floating flat square elements in an aligned arrangement. The Reynolds number based on the Taylor microscale is about 40 at a distance of 70 times the separation between the elements downstream of the grid; this value is comparable to that of many experiments.While the results compare relatively well with existing experimental data on grid turbulence (grid made up of bars), they highlight the importance of the mesh resolution of the simulation and computational domain size in the decay of turbulence. For example, while a power-law decay could be identified, at least over a short distance, its decay exponent proves to be difficult to determine with good accuracy. This points out the need for simulations (and perhaps experiments too) where all scales are properly solved before conclusions can be drawn.

MHD dynamo simulation using the GeoFEM platform—verification by the dynamo benchmark test

We verified a magnetohydrodynamic (MHD) simulation code in a rotating spherical shell using the parallel finite element method by comparing with the dynamo benchmark test by Christensen et al. [“A numerical dynamo benchmark”, Physics of Earth and Planetary Interiors, 128 (2001), 25–34]. We performed the non-magnetic case and dynamo with the insulated inner core case of the benchmark test. The results show that all results of the MHD case have <5% differences from the benchmark solutions. Only the drift frequency in the non-magnetic case duffers by more. This discrepancy is attributed to the small amplitude of the drift frequency in the non-magnetic case. We conclude that the present simulation code can represent dynamics and behavior of convection pattern and magnetic field although the present simulation model has some limitations such as the finite size of simulation domain.

Lattice-dynamical calculation of phonon scattering at ideal Si–Ge interfaces

Detailed phonon scattering at an ideal Si–Ge interface is studied with a linear lattice dynamics model. Frequency dependent transmission coefficients indicate the significance of acoustic-optical phonon mode conversion at the interface. Applied to multiple interfaces, the method shows how the overall thermal resistance approaches a finite (Bloch mode) limit with the increasing number of interfaces in absence of other scattering mechanisms. The dependence of thermal resistance on the superlattice layer thickness is not significant even in the interface-scattering-only limit we study. We also assess errors incurred by the finite domain size and classical statistics in molecular dynamics simulations of interface thermal resistance. Results suggest that using 6×6 unit cells in the transverse directions, a tractable size for such simulations, will incur only a 5% error in the predicted thermal resistance. Similarly, the error due to the classical (Boltzmann) phonon distribution in molecular dynamics simulations is predicted to be less than 10% for temperatures above 300 K.

A two-dimensional molecular dynamics simulation of liquid-vapor nucleation

The molecular dynamics method is employed to simulate the liquid-vapor nucleation processes. The results show that the initial stage of nucleus in nucleation process is cavity or space containing very few vapor molecules. Because of the very limited size of the simulation domain in previous reports, further growth of the nucleus has not been realized. Large scale molecular dynamics simulation of liquid-vapor nucleation indicates that the liquid-vapor nucleation process undergoes at least three stages: cavity growth, cavity coalescence, bubble formation.