Computational Cell Size Research Articles

Micromagnetic simulations of the size dependence of the Curie temperature in ferromagnetic nanowires and nanolayers

We solve the Landau-Lifshitz-Gilbert equation in the finite-temperature regime, where thermal fluctuations are modeled by a random magnetic field whose variance is proportional to the temperature. By rescaling the temperature proportionally to the computational cell size Δx (T→TΔx/aeff, where aeff is the lattice constant) [M. B. Hahn, J. Phys. Comm., 3:075009, 2019], we obtain Curie temperatures TC that are in line with the experimental values for cobalt, iron and nickel. For finite-sized objects such as nanowires (1D) and nanolayers (2D), the Curie temperature varies with the smallest size d of the system. We show that the difference between the computed finite-size TC and the bulk TC follows a power-law of the type: (ξ0/d)λ, where ξ0 is the correlation length at zero temperature, and λ is a critical exponent. We obtain values of ξ0 in the nanometer range, also in accordance with other simulations and experiments. The computed critical exponent is close to λ=2 for all considered materials and geometries. This is the expected result for a mean-field approach, but slightly larger than the values observed experimentally.

Methodology for Service Life Evaluation of Screens Welded Structures

The methodology of research on welded assemblies for fastening vibrators is based on modern software products, in particular SolidWorks Simulation in combination with SolidWorks Motion and hot spot stress (HSS) technology. It has been determined that the research on welded assemblies using the SolidWorks Education Edition software package is expedient, considering the most unfavorable situation, when there is a lack of fusion of edges. The solid-state model displays a lack of fusion as a gap between the welded parts. The research on the stress-strain state of welded structures using the finite element method shows that when the computational mesh cell size is reduced, the stress increases significantly, indicating the model singularity and the need for further application of the HSS technology. Research has revealed that the maximum stresses occur in those points of the welds where the longitudinal middle rib is connected to the plate and pipe. It has been determined that the service life of welded joints will exceed 2·106 cycles. To assess the accuracy of calculating the dynamic forces arising during the screen operation, the modeling results using the SolidWorks Motion program are compared with those classical methods that use the Lagrange equation of the second kind. It turned out that the calculation error does not exceed 30 %.

A methodological approach to assessing the durability of welded structures of screens using SolidWorks Simulation software

Purpose. To develop methodological recommendations for studying the characteristics of screen welded assemblies of ГВЧ-31 С type using specialized tools of the SolidWorks Education Edition software package. Methodology. The methodology for analyzing welds when designing a vibrator fixation system is based on the use of current software tools, in particular SolidWorks Simulation in combination with SolidWorks Motion, as well as the HOT SPOT STRESS technology. To analyze the accuracy of determining the dynamic loads arising during the screen operation, the results of modeling using the SolidWorks Motion program are compared with those obtained by traditional methods using the Lagrange equation of the second kind. The computation discrepancy is within 10 %. Findings. It has been determined that it is rational to analyze welds using the SolidWorks Education Edition software shell, taking into account the least profitable option, namely, when their edges are not finished. Furthermore, during solid-state modeling, the formation of a cavity in the weld is simulated in the form of a gap between the welded elements. The stress-strain state analysis of welded constructions using the Finite Element Method has revealed that when the computational mesh cell size is reduced, the stress value increases significantly, which indicates the result singularity and the need for further application of the HOT SPOT STRESS method. In the course of research, it has been determined that the highest stresses in welds occur on the central rib. The duration of use of welded joints is more than 2·106 cycles. Originality. For the first time, the methodology has been substantiated for determining the service life of welded elements of screen constructions using the latest computer analysis tools. The method makes it possible to calculate the dynamic forces arising in constructions performing oscillatory movements, as well as to analyze the stress-strain state of welds using the HOT SPOT STRESS technology and assess their service life. Practical value. It has become possible to implement the method for calculating the stress-strain state of welds in the design of a vibrator fixation system and assessing their service life, which is important for analyzing and determining the parameters of various vibrating machines. The results derived from the investigation were incorporated by the local entity, Ukrprommineral, to modernize the screens.

Subgrid-scale modeling of tsunami inundation in coastal urban areas

Numerical tsunami inundation simulations using high-resolution (HR) topographical data are important to predict tsunami damage in urban areas at individual building levels accurately but are challenging due to the high computational cost. To address this issue, a subgrid-scale (SGS) model of tsunami inundation, called the individual drag force model (iDFM), is developed. In this model, the sum of the building drag forces in a computational mesh is fed back to the flow field by taking into account spatial information about multiple structures in the mesh. To evaluate the model performance, idealized numerical experiments using simple urban topography with several types of spatial layout patterns and hindcast physical experiments focusing upon Onagawa Town affected by the 2011 Tohoku, Japan tsunami as a historical event are conducted. Results are compared with HR tsunami simulations using building-resolved topographical data, called the structure resolving model (SRM). In general, the iDFM (and other SGS models) characterizes the effects of structures as resistance elements that reduce the fluid velocity in momentum conservation. On the other hand, the SRM evaluates these effects as topography and feeds them back into not only momentum conservation but also mass conservation and wet/dry boundary conditions. Therefore, the iDFM can model the overall inundation characteristics, such as the limits of inundation, more than 10 2 times efficiently compared with the SRM, although it cannot capture local phenomena driven by structures, such as surface rising due to blocking and contracting current between structures. In both numerical and historical tsunami (Onagawa) cases, there were small differences between the modeled inundation characteristics, such as the maximum surface elevation and fluid velocity, and the time series of inundation leading edges determined by the iDFM due to the computational grid cell sizes. The observed differences between the idealized numerical experiment and the historical tsunami case can be affected by the drag coefficient and the Froude number during the tsunami run-up.

Effect of computational grid cell size and heterogeneity of computing area for estimated fire detection time

Introduction . In Russia, based on the provisions of the current regulatory documents, the time for the start of evacuation for a room in which a fire broke out is determined depending on the area of the room. According to some authors, the time of the start of the evacuation of people is a combination of “technical”, which includes the time of detection of a fire, and “psychophysical”, determined by the behavioral and organizational characteristics of the people who make it up. The fire detection time is currently not taken into account. Purpose . Evaluation of the influence of the size of the cells of the computational grid and the inhomogeneity of the computational domain on the estimated time of fire detection. Aims. 1. Establish the qualitative nature of the influence of the size of the cells of the computational grid and the inhomogeneity of the computational domain on the estimated time of fire detection. 2. Offer recommendations for determining the estimated time of fire detection. Methods . For research, computer simulation methods were used using the Fire Dynamics Simulator software package. Results and discussion . The use of grids with different cell sizes can significantly reduce the number of cells in the computational domain and, as a result, the computation time. However, this leads to rather contradictory results. The minimum time values are reduced by almost 3–4 times compared to a homogeneous computational grid, and the maximum time increases by 2 times. Conclusions . 1. The size of the cells of the computational grid and the inhomogeneity of the computational domain have a significant impact on the time of fire detection. 2. A sufficiently large spread in the values of the estimated fire detection time may indicate an unreliable estimate of the total time for the start of evacuation and incorrect conclusions about the safe evacuation of people and/or the probability of evacuation of people. 3. For a correct estimate of the evacuation start time, taken into account the estimated fire detection time, it is recommended to use homogeneous computational grids with cell sizes not exceeding 0.25 m.

Modeling droplet collision dynamic for Lagrangian simulation of impinging spray under high ambient pressures using an improved approach

Spray-to-spray impingement under ambient pressures of 10–60 atm was investigated numerically and experimentally, with particular interest in illustrating the influence of droplet collision dynamic on the spray characteristic. Specially, an improved approach for collision probability prediction was proposed by taking into account the initial size and distance of colliding droplets. The numerical simulations show our approach accounts for the collisions among droplets located in the different computational cells, hence producing substantial independence of computational cell size and total parcel number. The improved approach was subsequently implemented with a recently proposed pressure-dependent collision outcome model to simulate the impinging spray characteristics, the results were compared to the widely-used O’Rourke’s and Estrade et al.’s models. By implementing the improved approach with the pressure-dependent collision outcome model, our numerical simulations successfully reproduce the tendency that droplet bouncing is promoted with increasing ambient pressure, which has been fully recognized in the previous experimental and theoretical studies, however, rarely reflected in previous numerical works. Spray microcosmic characteristic was further discussed based on the numerical simulations.

Non-Premixed Filtered Tabulated Chemistry for LES: Evaluation on Sandia Flames D and E

The non-premixed filtered tabulated chemistry for large eddy simulations employs numerical filtering to resolve a thin flame front on practical LES numerical grids. The flame structure is modified to be coherent with the domain discretization. The first turbulent combustion application of the non-premixed filtered tabulated chemistry approach is presented. A keen comparison of the flamelet filtering transformation in the premixed and non-premixed regimes is carried out. Three distinctive features are outlined: the flame thickness variation, the filtered manifold transformation, and the model activation dependence on the chosen diffusion flamelet configuration for a non-premixed filtered approach. The model performance is assessed on two real turbulent flame configurations, Sandia flames D and E, employing a three-dimensional tabulation strategy, where the numerical grid is coupled with the model by the third parameter, i.e., the computational cell size. The repercussions of the above cited aspects are carefully assessed. The results demonstrate that the formalism coupling with an SGS modeling function can adequately describe wrinkled flame front effects. The predictions for both the major stable species and the minor ones accurately correspond with the underlying physics. It turns out that there is a substantial variation of the filter effect as a function of the strain rate of the flame and the considered species. The varying filter sensitivity along the manifold influences the response of the model correction terms and the retrieved variables. The non-premixed FTACLES formalism possibilities and conditions for the model’s utilization and optimal performance are clearly stated, to confirm the idea that SGS closure in diffusive combustion can be derived based on filtering arguments, and not only based on statistical approaches.

Understanding the effects of digital elevation model resolution and building treatment for urban flood modelling

Study regionA mountain city in the coastal region of Southeast China. Study focusThis study elucidated the effect of digital elevation model (DEM) resolution on flood simulation errors and inundation depth distributions through building treatment methods and river channel definition. The optimal DEM resolution was evaluated to determine whether satisfactory inundation simulation could be achieved for urban flash flood simulation (UFFS) and fluvial overbank flood simulation (FOFS).New hydrological insights for the region: UFFS and FOFS presented opposite effects regarding inundation extent and the spatial distribution of inundation depth with coarsening DEM resolution. In UFFS, the inundation extent and inundation depth in low-lying areas of the flood propagation pathway were underestimated. This effect was attributed to the change of local flood pathway caused by different treatment of buildings at coarser DEM resolution. The simulation error was magnified considerably when the DEM resolution was greater than the building width and gaps. In FOFS, owing to the changed channel geometry at coarser resolution, the inundation extent and inundation depth were overestimated. Using a DEM resolution and computational cell size that are lower than the river width is recommended. This study illustrated that a regional-scale effect, dependent on regional flood propagation behaviour and the impact of land use and topography on the flood propagation pathway, could be observed by coarsening the DEM resolution of inundation simulations.

Correction: Li et al. Joint Effects of the DEM Resolution and the Computational Cell Size on the Routing Methods in Hydrological Modelling. Water 2022, 14, 797

A new citation needs to be added to the original publication [...]

Joint Effects of the DEM Resolution and the Computational Cell Size on the Routing Methods in Hydrological Modelling

Natural disasters, including droughts and floods, have caused huge losses to mankind. Hydrological modelling is an indispensable tool for obtaining a better understanding of hydrological processes. The DEM-based routing methods, which are widely used in the distributed hydrological models, are sensitive to both the DEM resolution and the computational cell size. Too little work has been devoted to the joint effects of DEM resolution and computational cell size on the routing methods. This study aims to study the joint effects of those two factors on discharge simulation performance with two representative routing methods. The selected methods are the improved aggregated network-response function routing method (I-NRF) and the Liner-reservoir-routing method (LRR). Those two routing methods are combined with two runoff generation models to simulate the discharge. The discharge simulation performance is evaluated under the cross combination of four DEM resolutions (i.e., 90 m, 250 m, 500 m, and 1000 m) and fifty-six computational cell sizes (ranging from 5 arc-min to 60 arc-min). Eleven years of hydroclimatic data from the Jianxi basin (2000–2010) and the Shizhenjie basin (1983–1993) in China are used. The results show that the effects of the DEM resolution and the computational cell size are different on the I-NRF method and the LRR method. The computational cell size has nearly no influence on the performance of the I-NRF methods, while the DEM resolution does. On the contrary, the LRR discharge simulation performance decreases with oscillating values as the computational cell size increases, but is hardly affected by the DEM resolution. Furthermore, the joint effects of the DEM resolution and the computational cell size can be ignored for both routing methods. The results of this study will help to establish the appropriate DEM resolution, computational cell size, and routing method when researchers build hydrological models to predict future disasters.

Molecular static simulation of edge dislocation core in bcc iron

We simulate the dislocation core structure in bcc iron using the modified Molecular Static method. A feature of this method is the application of an iterative procedure in which the atomic structure in the vicinity of the defect and the constants that determine the displacements of atoms immersed in the elastic continuum are calculated in a self-consistent manner. Following the mentioned approach, we develop a model for calculating the atomic structure of edge dislocations, taking into account the anisotropy of the elastic medium surrounding the main calculation cell. Anisotropy is taken into account by introducing an explicit angular dependence for the parameters of the elastic field created by the dislocation: magnitude of Burgers vector and Poisson’s ratio. Simulation is carried out for a split dislocation with Burgers vector along [100]. The convergence of the iterative algorithm is shown and the influence of the computational cell size on the results is considered. Calculated results are: atomic structure of dislocation in bcc iron, angular dependence of the parameters describing the elastic dislocation field at large distances from the dislocation line, and the strain tensor components in the entire simulation area.

A chimera approach for MP-PIC simulations of dense particulate flows using large parcel size relative to the computational cell size

The Multiphase Particle in Cell (MP-PIC) is an Eulerian-Lagrangian numerical method that resolves the particle-particle interactions using the averages mapped from the Lagrangian parcels onto the Eulerian mesh. The MPPIC's accuracy depends on mesh quality and resolution, but the mesh resolution requirements for the Computational Fluid Dynamics (CFD) fields and MP-PIC models are not in accordance. This paper proposes a chimera approach, which implements two overlapping meshes in the Lagrangian-Eulerian framework with disparate length scales - a fine mesh for the CFD fields and a coarser mesh for the MP-PIC fields. The CFD fields are mapped to the MP-PIC mesh, while the coarse mesh fields, such as solids volume fraction and momentum source of parcels, are mapped to the finer CFD mesh. The National Energy Technology Laboratory's (NETL) Small-Scale Challenge Problems-I (SSCP-I) fluidized bed case is selected for simulations and model validation. A parametric study is conducted, which considers different drag and inter-particle stress models and different solids volume fraction limits. We show that the chimera approach results in a realistic turbulent flow field for accurate drag force calculations on parcels while preserving adequate conditions for the submodels’ validity under MP-PIC. The results are in good agreement with the experimental findings, specifically the pressure drop, Eulerian average particle velocity, and granular temperature. The chimera method is developed to overcome the averaging limitations when the particle size is comparable to the cell size or when particle collisions may not be captured accurately, and a finer mesh is required for the fluid flow.

Improving Time Step Convergence in an Atmosphere Model With Simplified Physics: Using Mathematical Rigor to Avoid Nonphysical Behavior in a Parameterization

AbstractGlobal atmospheric models seek to capture physical phenomena across a wide range of time and length scales. For this to be a feasible task, the physical processes with time or length scales below that of a computational time step or grid cell size are simplified as one or more parameterizations. Inadvertent oversimplification can violate constraints or destroy relationships in the original physical system and consequently lead to unexpected and physically invalid behavior. An example of such a problem has been investigated in the work of Wan et al. (2020, https://doi.org/10.1029/2019MS001982). This work addresses the issues at a more fundamental level by revisiting the parameterization derivation. A derivation of an unaveraged condensation rate in the unaveraged equations, sometimes referred to as subgrid equations, provides a clear description and more accurate quantification of the condensation/evaporation processes associated with cloud growth/decay, while avoiding simplifications used in earlier studies. A subgrid reconstruction (SGR) methodology is used to connect the unaveraged condensation rate with the grid cell averaged equations solved by the global model. Analyses of the SGR method and the numerical results provide insights into root causes of inconsistent discrete formulations and nonphysical behavior. It is also shown that the SGR methodology provides a flexible framework for addressing such inconsistencies. This work serves as a demonstration that when nonphysical behavior in a parameterization of subgrid variability is avoided through rigorous mathematical derivation, the resulting formulation can exhibit both better numerical convergence properties and significant impact on long‐term climate.

Numerical Study of Sediment Flow Over Bottom Intake Racks With Flow-3D

Bottom intakes are the most useful structure for diverting the flow of steep rivers and providing specific amount of water for hydropower usage. It is crucial to obtain optimum of physical parameters in order to divert desired discharge with minimum possibility of occlusion. Numerical models can simulate flow and turbulence transport equations at any complex geometries. Numerical methods based on Computational Fluid Dynamics (CFD), are one of the most common methods of numerical simulation that is used in water structures. According to the capabilities of numerical methods, complex modes of flow field over bottom intakes can be analyzed. In the present study, Flow-3D software is used to investigate the experimental results of the previous researcher for sediment and clean water flow over bottom intake with circular bars numerically. This study is carried out in a total of 27 models for clean water and 9 models of sediment flow (Bed-Load) at different approaching flow conditions. Parameters of roughness, size of computational cell, turbulence transport equation, Bed Load Transport equation and bed load coefficient has been calibrated. Validation procedure proved that the accuracy and performance of numerical models appear to be acceptable for designing intake systems. For each test, the discharge coefficient is computed, then by using dimensional analysis, a dimensionless relation derived from the dependent and independent variables and compared with the measured discharge coefficient. Estimating the discharge coefficient by the proposed equation in clean water flow performed a mean error of 6.4 percent and for sediment flow led to a mean error of 4.3 percent.

Magnetohydrodynamic simulation code CANS+: Assessments and applications

Abstract We present a new magnetohydrodynamic (MHD) simulation package with the aim of providing accurate numerical solutions to astrophysical phenomena where discontinuities, shock waves, and turbulence are inherently important. The code implements the Harten–Lax–van Leer–discontinuitues (HLLD) approximate Riemann solver, the fifth-order-monotonicity-preserving interpolation (MP5) scheme, and the hyperbolic divergence cleaning method for a magnetic field. This choice of schemes has significantly improved numerical accuracy and stability, and saved computational costs in multidimensional problems. Numerical tests of one- and two-dimensional problems show the advantages of using the high-order scheme by comparing with results from a standard second-order total variation diminishing monotonic upwind scheme for conservation laws (MUSCL) scheme. The present code enables us to explore the long-term evolution of a three-dimensional accretion disk around a black hole, in which compressible MHD turbulence causes continuous mass accretion via nonlinear growth of the magneto-rotational instability (MRI). Numerical tests with various computational cell sizes exhibits a convergent picture of the early nonlinear growth of the MRI in a global model, and indicates that the MP5 scheme has more than twice the resolution of the MUSCL scheme in practical applications.

Theoretical Analysis of Computational Fluid Dynamics–Discrete Element Method Mathematical Model Solution Change With Varying Computational Cell Size

Successful verification and validation is crucial to build confidence in the application of coupled computational fluid dynamics–discrete element method (CFD–DEM). Model verification includes ensuring a mesh-independent solution, which poses a major difficulty in CFD–DEM due to the complicated relationship between solution and computational cell size. In this paper, we investigate the production of numerical error in the CFD–DEM coupling procedure with computational grid refinement. The porosity distribution output from simulations of fixed-particle beds is determined to be Gaussian, and the average and standard deviation of the representative distribution are reported against cell size. We find that the standard deviation of bed porosity increases exponentially as the cell size is reduced. The average drag calculated from each drag law is very sensitive to changes in the porosity standard deviation. When combined together, these effects result in an exponential change in expected drag force when the cell size is small relative to the particle diameter. The divided volume fraction method of porosity calculation is shown to be superior to the centered volume fraction (CVF) method. The sensitivity of five popular drag laws to changes in the porosity distribution is presented, and the Ergun and Beetstra drag laws are shown to be the least sensitive to changes in the cell size. A cell size greater than three average particle diameters is recommended to prevent errors in the simulation results. A grid refinement study (GRS) is used to quantify numerical error.

A CFD hybrid approach to simulate liquid-phase chemical reactors

Design and safety assessments of chemical reactors can be done using Reynolds Averaged Navier-Stokes (RANS) type equations. The averaging procedure of transport equations gives rise to unclosed terms, which must be properly modeled independently on the computational cell size. In particular, presence of chemical reactions leads to an additional source term in species equation. The averaged value of this term involves effects of both chemical kinetics and turbulence. Turbulence-kinetics interaction (TKI) models must be then developed in order to close species transport equations, so that Computational Fluid Dynamics (CFD) can be used to reduce the number of experiments required to design a chemical reactor.Many TKI models have been developed in the past, mainly for gaseous systems, while liquid-phase models have been less investigated because of demanding theoretical challenges. Therefore, the purpose of this work is the development of a new TKI model for liquid phase reactions, which combines the Laminar Rate model (for kinetic controlled systems) with the Multiple Time Scales model (for turbulence controlled systems) allowing its use also when kinetic and turbulent mixing characteristic times are comparable. An analysis of the influence of the turbulence model coupled with the proposed model was carried out to identify the most suitable turbulence model, and two different case studies were investigated to show the potentialities of the proposed approach.

The Thermal Conductivity of Magnesite, Dolomite and Calcite as Determined by Molecular Dynamics Simulation

In this study, the phonon-based thermal conductivity of magnesite (MgCO3) and dolomite (CaMg(CO3)2) is calculated and compared with an earlier recent calculation on calcite (CaCO3). Equilibrium molecular dynamics simulation by way of the elegant Green-Kubo formalism is used for calculating the thermal conductivity. The thermal conductivity is investigated over a wide temperature range (from 200 K to 800 K) for all of the above mentioned materials. The most reliable potential parameters are used for characterising the interatomic interactions. In all of the models, two independent mechanisms are considered. The first is temperature independent, which is relevant to the acoustic short-range and optical phonons, and the other is temperature dependent, which is linked to the acoustic long-range phonons. In the study, the heat current autocorrelation function (HCACF) is calculated over the averages of the NPT, NVT and NVE ensembles in the x- and z- directions. In addition, it is shown that the optical, acoustic short- and long-range phonon modes are the main contributors to the decomposition model of the thermal conductivity. In a further investigation, the effects of the computational cell sizes on the thermal conductivity are investigated with five different simulation blocks containing 30, 240, 810, 1920 and 6480 atoms. Finally, this research provides a comparison of the thermal conductivity from this study and experimental studies: they are in good agreement.

How Computational Grid Refinement in Three Dimensions Affects Computational Fluid Dynamics-Discrete Element Method Results for Psuedo-Two-Dimensional Fluidized Gas–Solid Beds

Computational fluid dynamics (CFD)-discrete element method (DEM) simulations are designed to model a pseudo-two-dimensional (2D) fluidized bed, in which bed thickness is minimal compared to height and length. Predicted bed behavior varies as the simulations are conducted on increasingly refined computational grids. Pseudo-2D simulation results, in which a single computational cell spans the bed thickness, are compared against fully-three-dimensional (3D) simulations results. Both pseudo-2D and fully-3D simulations exhibit high accuracy when sufficiently refined. Indicators of bed behavior, such as bed height, bed height fluctuation, bubble generation frequency, and segregation, do not appear to converge as the cell size is reduced. The Koch-Hill and Gidaspow drag laws are alternately employed in the simulations, resulting in different trends of results with computational grid refinement. Grid refinement studies are used to quantify the change in results with grid refinement for both three-dimensional, uniform refinement, and for two-dimensional refinement on pseudo-2D computational grids. Grid refinement study results indicate the total drag converges as the computational grid is refined, for both 3D and pseudo-2D approaches. The grid refinement study results are also used to distinguish the relatively grid-independent results using the Koch-Hill drag law from the highly grid-dependent Gidaspow drag law results. Computational cell size has a significant impact on CFD-DEM results for fluidized beds, but the grid refinement study method can be used to quantify the resulting numerical error.

Assessment of CFD-DEM solution error against computational cell size for flows through a fixed-bed of binary-sized particles

Computational cell size is a crucial factor for accuracy in Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations of particle-fluid interactions. In the present study, we investigate how simulation results change with computational cell size and mixture composition, for calculation of drag force over a fixed bed containing a binary-sized particle mixture. To investigate the complex solution convergence behavior, the simulation results are examined for several definitions of dimensionless computational cell size. Several regimes of consistent behavior, across three investigated mixtures, are identified and a consistently optimal cell size range is identified. We find that both the difference between simulated solution results and published experimental results, and the standard deviation of the void fraction profile, show consistent trends when plotted against the dimensionless computational cell size based on the Sauter-mean particle diameter. Grid-refinement studies are performed across all grid solutions, and the Grid Convergence Index (GCI) is analyzed as a predictor for the grid solution error. Correlations between simulation error and GCI are not strong, likely because of incongruence of the solution trends with typical asymptotic convergence. Alternatively, a correlation between change in solution value on successively refined grids and finer-grid solution error is shown to be adequate for the current results.