Number Of Simulation Particles Research Articles

Adaptive symplectic model order reduction of parametric particle-based Vlasov–Poisson equation

High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of parameters. In this work, we derive reduced order models for the semi-discrete Hamiltonian system resulting from a geometric particle-in-cell approximation of the parametric Vlasov–Poisson equations. Since the problem’s nondissipative and highly nonlinear nature makes it reducible only locally in time, we adopt a nonlinear reduced basis approach where the reduced phase space evolves in time. This strategy allows a significant reduction in the number of simulated particles, but the evaluation of the nonlinear operators associated with the Vlasov–Poisson coupling remains computationally expensive. We propose a novel reduction of the nonlinear terms that combines adaptive parameter sampling and hyper-reduction techniques to address this. The proposed approach allows decoupling the operations having a cost dependent on the number of particles from those that depend on the instances of the required parameters. In particular, in each time step, the electric potential is approximated via dynamic mode decomposition (DMD) and the particle-to-grid map via a discrete empirical interpolation method (DEIM). These approximations are constructed from data obtained from a past temporal window at a few selected values of the parameters to guarantee a computationally efficient adaptation. The resulting DMD-DEIM reduced dynamical system retains the Hamiltonian structure of the full model, provides good approximations of the solution, and can be solved at a reduced computational cost.

Fluidized bed gas-solid heat transfer using a CFD-DEM coarse-graining technique

Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) is extensively used for modeling heat transfer in gas-solid fluidized beds. However, CFD-DEM is computationally expensive, leading to a restriction regarding the number of simulated particles. Coarse-grained CFD-DEM is a technique to circumvent this constraint, allowing one to simulate larger fluidized beds. In this work, a scaling law used for coarse-graining hydrodynamics is generalized to gas-solid heat-transfer. This approach for coarse-graining heat transfer is tested using three different superficial gas velocities where the coarse-grained particle temperatures and Nusselt numbers are obtained. The particle temperature shows good correspondence with the original system for all cases and the Nusselt number is accurately predicted by the coarse-graining scaling law.

Numerical modelling of SS316L powder flowability for laser powder-bed fusion

This work aims to improve the powder-bed spreading process for laser powder bed fusion additive manufacturing by gaining a greater understanding of metal powder flowability through numerical modelling and in-situ experimentation.Using the Discrete Element Method (DEM) to study the flowability of the powder and its intrinsic properties. A high-fidelity particle-scale model was developed to capture the dynamics of metal particle interactions in a virtual Hall flow meter based on a modified Beverloo law. The results are validated experimentally using the Hall flow static powder characterisation technique.For SS316L powder alloy with the hall-value of 29s/50g and with an angle of repose (AOR) of 32, the modelled powder that exhibited the same flow behaviour was found using 0.5 for both rolling and sliding coefficients resulting in simulated Hall value of 28.55s/50g with a simulated flow rate of 0.571 g/s, which is validated by AOR of the simulated powder [31.2-32.6]. However, rolling friction had minimal effect on the mass flow rate but increased the angle of repose. Sliding friction significantly decreased the mass flow rate and increased AOR.DEM is an ideal method to study flowability. However, there are certain constraints imposed on the computational power by a number of simulated particles and simulation time-step. Future research may involve investigating other dynamic flowability characterisation techniques.Enabling a better understanding of powder particle flow at a micro-scale by modelling powder flowability. This leads to simulating a more realistic powder bed and improving the powder spreading process, leading to better AM parts quality.This paper provides a unique approach for modelling the flowability of SS316L powder using a Beverloo law-based design of the Hall flow meter. This will improve the modelling of the spreading process needed for metal 3D printing.

A detailed gas-solid fluidized bed comparison study on CFD-DEM coarse-graining techniques

Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) is a numerical tool used for detailed fluidized bed studies. However, CFD-DEM is computationally expensive, leading to a restriction regarding the number of simulated particles. Therefore, coarse-graining techniques have been developed to increase the simulation scale or reduce computational requirements for CFD-DEM simulations in fluidized beds. In this work, we critically compared the coarse-graining scaling laws of Mu et al. [2020, Chemical Engineering Science: X 6.] and Sakai and Koshizuka [2009, Chemical Engineering Science: 64, 533–539.] for their effectiveness in characterizing the original system. The first mentioned approach was not able to accurately characterize the original system, while the latter methodology showed good correspondence. We also demonstrated that applying a continuous two-way smoothing function to the coarse-graining process can yield grid-independent solutions, particularly when the particle diameter is much larger than the grid cell size, which is often the case in CFD-DEM simulations.

Improved Algorithms for Calculating the Space-Charge Field in Vacuum Devices

The space-charge field (SCF) is a key factor in vacuum electronic devices, accelerators, free electron lasers and plasma systems, etc. The calculation of the SCF is very important since it has a great influence on the precision of numerical simulation results. However, calculating the SCF usually takes a lot of time, especially when the number of simulated particles is large. In this paper, we used a vectorization, parallelization and truncation method to optimize the calculation of the SCF based on the traditional calculation algorithms. To verify the validity of the optimized SCF calculation algorithm, it was applied in the performance simulation of a millimeter wave traveling wave tube. The results showed that the time cost was reduced by three orders compared with conventional treatment. The proposed algorithm also has great potential applications in free electron lasers, accelerators and plasma systems.

Time analysis of regional structure of large-scale particle using an interactive visual system

N-body numerical simulation is an important tool in astronomy. Scientists used this method to simulate the formation of structure of the universe, which is key to understanding how the universe formed. As research on this subject further develops, astronomers require a more precise method that enables expansion of the simulation and an increase in the number of simulation particles. However, retaining all temporal information is infeasible due to a lack of computer storage. In the circumstances, astronomers reserve temporal data at intervals, merging rough and baffling animations of universal evolution. In this study, we propose a deep-learning-assisted interpolation application to analyze the structure formation of the universe. First, we evaluate the feasibility of applying interpolation to generate an animation of the universal evolution through an experiment. Then, we demonstrate the superiority of deep convolutional neural network (DCNN) method by comparing its quality and performance with the actual results together with the results generated by other popular interpolation algorithms. In addition, we present PRSVis, an interactive visual analytics system that supports global volume rendering, local area magnification, and temporal animation generation. PRSVis allows users to visualize a global volume rendering, interactively select one cubic region from the rendering and intelligently produce a time-series animation of the high-resolution region using the deep-learning-assisted method. In summary, we propose an interactive visual system, integrated with the DCNN interpolation method that is validated through experiments, to help scientists easily understand the evolution of the particle region structure.

Influence of initial particle configuration upon sphericity of shock loaded density interface in SPH modelling of Richtmyer-Meshkov instability

The Richtmyer-Meshkov Instability (RMI) occurs when a perturbed interface between two fluids of different densities undergoes impulsive acceleration by, for example, a shock wave. Its study is important for gaining better understanding of processes governing inertial confinement fusion where a spherical solid deuterium-tritium (DT) capsule filled with the DT gas is compressed by a powerful laser [1]. The imploding shock moving to the center of the spherical shell causes the RMI to form on its inner surface due to a large density difference between solid and gaseous DT phases, which leads to a rapid growth of initially present randomperturbations. Usually, the density interface consists of random perturbations (e.g., surface roughness, machining inaccuracies, etc.) which initially grow linearly before nonlinear effects emerge. To improve reliability of shock-driven flow simulations, it is necessary to understand the factors which inuence the RMI growth. Our work aims to find the best initial particle configuration that does not introduce artificial perturbations of the spherical density interface. The shocked interface must preserve spherical symmetry if no perturbations are applied. In order to reduce the number of simulated particles in calculation, it is necessary to adapt spatial resolution, i.e., to increase the concentration of particles in target regions.

Single neutron tracking method for calculating the probability of survival based on the RMC code

In a weak neutron source system, the neutron chains rarely overlap, and hence the neutrons should be described by stochastic kinetics. The probability of survival (POS) is a quantity that is often calculated in the field of stochastic kinetics and is also a simple index to test the correctness of the method of describing weak source systems. The general Monte Carlo method for calculating POS needs to control the number of simulated particles, which introduces deviations. In this work, an innovative single neutron tracking method for calculating POS based on the Reactor Monte Carlo (RMC) code is proposed, and it does not need to control the number of particles. The relative difference between the POS calculated by RMC and those calculated by MCATK are less than 6%. The new method is more accurate and user-friendly than the traditional method.

Deep Representation of a Normal Map for Screen-Space Fluid Rendering

We propose a novel method for addressing the problem of efficiently generating a highly refined normal map for screen-space fluid rendering. Because the process of filtering the normal map is crucially important to ensure the quality of the final screen-space fluid rendering, we employ a conditional generative adversarial network (cGAN) as a filter that learns a deep normal map representation, thereby refining the low-quality normal map. In particular, we have designed a novel loss function dedicated to refining the normal map information, and we use a specific set of auxiliary features to train the cGAN generator to learn features that are more robust with respect to edge details. Additionally, we constructed a dataset of six different typical scenes to enable effective demonstrations of multitype fluid simulation. Experiments indicated that our generator was able to infer clearer and more detailed features for this dataset than a basic screen-space fluid rendering method. Moreover, in some cases, the results generated by our method were even smoother than those generated by the conventional surface reconstruction method. Our method improves the fluid rendering results via the high-quality normal map while preserving the advantages of the screen-space fluid rendering methods and the traditional surface reconstruction methods, including that of the computation time being independent of the number of simulation particles and the spatial resolution being related only to image resolution.

Scalable Graph Networks for Particle Simulations

Learning system dynamics directly from observations is a promising direction in machine learning due to its potential to significantly enhance our ability to understand physical systems. However, the dynamics of many real-world systems are challenging to learn due to the presence of nonlinear potentials and a number of interactions that scales quadratically with the number of particles N, as in the case of the N-body problem. In this work we introduce an approach that transforms a fully-connected interaction graph into a hierarchical one which reduces the number of edges to O(N). This results in a linear time and space complexity while the pre-computation of the hierarchical graph requires O(N log (N)) time and O(N) space. Using our approach, we are able to train models on much larger particle counts, even on a single GPU. We evaluate how the phase space position accuracy and energy conservation depend on the number of simulated particles. Our approach retains high accuracy and efficiency even on large-scale gravitational N-body simulations which are impossible to run on a single machine if a fully-connected graph is used. Similar results are also observed when simulating Coulomb interactions. Furthermore, we make several important observations regarding the performance of this new hierarchical model, including: i) its accuracy tends to improve with the number of particles in the simulation and ii) its generalisation to unseen particle counts is also much better than for models that use all O(N^2) interactions.

Collisional growth in a particle-based cloud microphysical model: insights from column model simulations using LCM1D (v1.0)

Abstract. Lagrangian cloud models (LCMs) are considered the future of cloud microphysical modelling. Compared to bulk models, however, LCMs are computationally expensive due to the typically high number of simulation particles (SIPs) necessary to represent microphysical processes such as collisional growth of hydrometeors successfully. In this study, the representation of collisional growth is explored in one-dimensional column simulations, allowing for the explicit consideration of sedimentation, complementing the authors' previous study on zero-dimensional collection in a single grid box. Two variants of the Lagrangian probabilistic all-or-nothing (AON) collection algorithm are tested that mainly differ in the assumed spatial distribution of the droplet ensemble: the first variant assumes the droplet ensemble to be well-mixed in a predefined three-dimensional grid box (WM3D), while the second variant considers the (sub-grid) vertical position of the SIPs, reducing the well-mixed assumption to a two-dimensional, horizontal plane (WM2D). Since the number of calculations in AON depends quadratically on the number of SIPs, an established approach is tested that reduces the number of calculations to a linear dependence (so-called linear sampling). All variants are compared to established Eulerian bin model solutions. Generally, all methods approach the same solutions and agree well if the methods are applied with sufficiently high resolution (foremost is the number of SIPs, and to a lesser extent time step and vertical grid spacing). Converging results were found for fairly large time steps, larger than those typically used in the numerical solution of diffusional growth. The dependence on the vertical grid spacing can be reduced if AON-WM2D is applied. The study also shows that AON-WM3D simulations with linear sampling, a common speed-up measure, converge only slightly slower compared to simulations with a quadratic SIP sampling. Hence, AON with linear sampling is the preferred choice when computation time is a limiting factor. Most importantly, the study highlights that results generally require a smaller number of SIPs per grid box for convergence than previous one-dimensional box simulations indicated. The reason is the ability of sedimenting SIPs to interact with a larger ensemble of particles when they are not restricted to a single grid box. Since sedimentation is considered in most commonly applied three-dimensional models, the results indicate smaller computational requirements for successful simulations, encouraging a wider use of LCMs in the future.

Numerical and experimental investigation on the performance of a ventilated chamber for low-cost PM sensor calibration

Particulate matter (PM) sensors are popular for distributed monitoring due to their portability, low-cost and networking capabilities. To provide reliable data, these sensors have to be calibrated periodically in the laboratory. This is often done in chambers with several of them co-located, alongside several research grade instruments. It is important to confirm that the aerosol is well distributed to ensure reliability and accuracy of the calibration tests. This paper describes a modeling and experimental study of these chambers used for calibration of PM sensors. The experimental setup is described and calibration results for the low-cost PM sensors (MAXIMA sensor, Applied Particle Technology, Inc.) using research-grade instruments (GRIMM 11-C, GRIMM Technologies, Inc.) are presented. A computational fluid dynamics (CFD) model including effects of turbulence and Brownian motion is used to predict particle trajectories and distribution in the chamber. The simulated particle number concentration agrees well with the measured values in the chamber. Having the CFD model, the suitability of three proposed chamber designs (fan off; fan on-parallel; fan on-diagonal) are explored for a variety of conditions. Operating conditions that result in uniform concentrations are established using the model. The recommended design for the PM sensor calibration in a rectangular ventilated chamber is: parallel fan layout, fan pressure of 12 Pa, and inlet air flow rate between 10 and 15 L/min. This study shows that the numerical modeling is available to understand the performance of a calibration chamber as well as optimizing the chamber design. A broader perspective is that the results validate the use of low-cost PM sensors for checking the distribution of aerosols in chambers.

Ghost‐Mirror Approach for Accurate and Efficient Kinetic Monte Carlo Simulation of Seeded Emulsion Polymerization

AbstractThe kinetic Monte Carlo (kMC) method is well suited to the simulation of seeded emulsion polymerization reactions. Inadequate simulation volume results in an incorrect radical entry rate, and as such that inaccuracy propagates into the particle phase simulation. A novel kMC method is described here that has coined the Ghost‐Mirror approach (GM‐kMC) to guarantee sufficient aqueous phase simulation volume while minimizing the number of dispersed phase environments, and while maintaining accuracy and consistency with results produced by kMC simulations. To do so, a subset of a kMC method is replicated where only the aqueous phase reactions are treated in that extended volume; particle phases in those replicated volumes are untreated, as “ghosts”. In doing so, a critical condition for aqueous phase simulation volume is calculated to yield accurate results in the overall system. Important to emphasize though is that one does not require the equivalent number of simulated particles in the GM‐kMC approaches. The required number of particles to simulate accurate results can be even orders of magnitude smaller than the kMC approach; inherently offering significant gains in computational efficiency. This is extended further, reducing the required simulation time, by a hybrid extension to this GM‐kMC method.

Robust Monte-Carlo Simulations in Diffusion-MRI: Effect of the Substrate Complexity and Parameter Choice on the Reproducibility of Results.

Monte-Carlo Diffusion Simulations (MCDS) have been used extensively as a ground truth tool for the validation of microstructure models for Diffusion-Weighted MRI. However, methodological pitfalls in the design of the biomimicking geometrical configurations and the simulation parameters can lead to approximation biases. Such pitfalls affect the reliability of the estimated signal, as well as its validity and reproducibility as ground truth data. In this work, we first present a set of experiments in order to study three critical pitfalls encountered in the design of MCDS in the literature, namely, the number of simulated particles and time steps, simplifications in the intra-axonal substrate representation, and the impact of the substrate's size on the signal stemming from the extra-axonal space. The results obtained show important changes in the simulated signals and the recovered microstructure features when changes in those parameters are introduced. Thereupon, driven by our findings from the first studies, we outline a general framework able to generate complex substrates. We show the framework's capability to overcome the aforementioned simplifications by generating a complex crossing substrate, which preserves the volume in the crossing area and achieves a high packing density. The results presented in this work, along with the simulator developed, pave the way toward more realistic and reproducible Monte-Carlo simulations for Diffusion-Weighted MRI.

EGSnrc application for IMRT planning.

The aim of this study was to describe a detailed instruction of intensity modulated radiotherapy (IMRT) planning simulation using BEAMnrc-DOSXYZnrc code system (EGSnrc package) and present a new graphical user interface based on MATLAB code (The MathWorks) to combine more than one. 3ddose file which were obtained from the IMRT plan. This study was performed in four phases: the commissioning of Varian Clinac iX6MV, the simulation of IMRT planning in EGSnrc, the creation of in-house VDOSE GUI, and the analysis of the isodose contour and dose volume histogram (DVH) curve from several beam angles. The plan paramaters in sequence and control point files were extracted from the planning data in Tan Tock Seng Hospital Singapore (multileaf collimator (MLC) leaf positions - bank A and bank B, gantry angles, coordinate of isocenters, and MU indexes). VDOSE GUI which was created in this study can display the distribution dose curve in each slice and beam angle. Dose distributions from various MLC settings and beam angles yield different dose distributions even though they used the same number of simulated particles. This was due to the differences in the MLC leaf openings in every field. The value of the relative dose error between the two dose ditributions for "body" was 51.23 %. The Monte Carlo (MC) data was normalized with the maximum dose but the analytical anisotropic algorithm (AAA) data was normalized by the dose in the isocenter. In this study, we have presented a Monte Carlo simulation framework for IMRT dose calculation using DOSXYZnrc source 21. Further studies are needed in conducting IMRT simulations using EGSnrc to minimize the different dose error and dose volume histogram deviation.

Comparison of modern implementations of the direct simulation Monte Carlo method

In this work, collisional schemes of the direct simulation Monte Carlo (DSMC) method are compared. The sensitivity of the schemes to the number of simulated particles is investigated. The original No-Time-Counter (NTC) scheme, proposed by G.A. Bird, its modification NTC-2007 and majorant collision frequency (MCF) scheme, proposed by M. S. Ivanov and S.V. Rogasinsky are considered. For the high-speed Couette flow with parameters corresponding to a near-continuum regime (speed ratio S is equal to 10, Knudsen number Kn is equal to 0.01) the convergence of shear stress component is analysed. Calculations with different total number of the simulated particles (in the range from 500 to 106) were performed. It was shown, that the deviation of NTC-2007 scheme from the reference solution is about four times larger as compared to the MCF scheme. The original NTC scheme exhibits much higher sensitivity to the number of simulated particles.

Mitigating inherent noise in Monte Carlo dose distributions using dilated U-Net.

Monte Carlo (MC) algorithms offer accurate modeling of dose calculation by simulating the transport and interactions of many particles through the patient geometry. However, given their random nature, the resulting dose distributions have statistical uncertainty (noise), which prevents making reliable clinical decisions. This issue is partly addressable using a huge number of simulated particles but is computationally expensive as it results in significantly greater computation times. Therefore, there is a trade-off between the computation time and the noise level in MC dose maps. In this work, we address the mitigation of noise inherent to MC dose distributions using dilated U-Net - an encoder-decoder-styled fully convolutional neural network, which allows fast and fully automated denoising of whole-volume dose maps. We use mean squared error (MSE) as loss function to train the model, where training is done in 2D and 2.5D settings by considering a number of adjacent slices. Our model is trained on proton therapy MC dose distributions of different tumor sites (brain, head and neck, liver, lungs, and prostate) acquired from 35 patients. We provide the network with input MC dose distributions simulated using particles while keeping particles as reference. After training, our model successfully denoises new MC dose maps. On average (averaged over five patients with different tumor sites), our model recovers of 55.99Gy from the noisy MC input of 49.51Gy, whereas the low noise MC (reference) offers 56.03Gy. We observed a significant reduction in average RMSE (thresholded >10% max ref) for reference vs denoised (1.25Gy) than reference vs input (16.96Gy) leading to an improvement in signal-to-noise ratio (ISNR) by 18.06dB. Moreover, the inference time of our model for a dose distribution is less than 10s vs 100min (MC simulation using particles). We propose an end-to-end fully convolutional network that can denoise Monte Carlo dose distributions. The networks provide comparable qualitative and quantitative results as the MC dose distribution simulated with particles, offering a significant reduction in computation time.

Effects of number of simulated particles on the uncertainty in simulation of dispersion of radioactive material using FLEXPART program

FLEXPART software simulates atmospheric emissions based on wind-field movements and random disturbances. To simulate random processes, FLEXPART uses a certain number of simulation particles. Changing the number of simulation particles causes a change in the simulated results of the dispersion concentration of the radionuclides. The larger number of simulated particles results in the more accurate simulated results. However, increasing the number of simulated particles results in the increasing of the computational cost. The report presents an assessment of the uncertainty in theconcentration of radionuclides in simulating dispersion of 137Cs and 131I nuclides using FLEXPART software according to the number of simulation particles. The number of simulation particles used in this study are 100, 1000, 5000, 7500, 10000, 15000, 20000, 25000 and 30000 particles / hour. Using the image processing software OpenCV to evaluate the uncertainties of simulated results according to the number of simulated particles used. Evaluation results show that the simulated results are acceptable with the number of simulated particles being of 20000 particles/hour.

Improved Modeling of Material Deposition during OLED Manufacturing Using Direct Simulation Monte Carlo Method on GPU Architecture

A direct simulation Monte Carlo (DSMC) method is implemented on graphical processing unit (GPU) architecture to simulate the deposition phenomena that occur on a glass panel during modern organic light emitting diodes (OLED) manufacturing processes with a huge number of simulated particles because a fully three-dimensional (3D) particle simulation is required to accurately predict deposition thickness and uniformity on the substrate in a low-pressure environment. To examine the accuracy and efficiency of the newly developed DSMC code running on GPU architecture, verification and validation tests were performed by solving several benchmarking problems. Under three conditions which have been applied in previous OLED deposition process test experiments, the new DSMC model successfully simulates the transport of organic material evaporated from the heated nozzle array and its deposition onto a glass panel inside a low-pressure chamber. The uniformity and normalized thickness between the DSMC and experimental results for the three test cases are then compared. The normalized thickness of the organic material deposited to the large glass panel calculated from the DSMC is found to have an error of less than 4%, and the uniformity values calculated from the absolute deposition thickness show good agreement with those obtained from experimental data in all test cases.

Model description of a two-dimensional electrostatic particle-in-cell simulation parallelized with a graphics processing unit for plasma discharges

Many key aspects of low-temperature plasmas include nonlinear, transient, and kinetic effects related to the spatio-temporal variation of electron energy distribution function (EEDF) which cannot be treated in a fluid simulation model. The particle-in-cell (PIC) simulation calculates kinetic effects through the statistical representation of the EEDF using many particles and thus gives accurate results. However, the computational cost is very expensive to resolve all aspects in a plasma discharge with millions of computational particles as well as hundreds of thousands of grids during millions of time steps. Additionally, the simulation of discharge plasmas should handle the collision processes and the rapid increase in the total number of simulation particles. In this presentation, details of a two-dimensional PIC simulation parallelized with graphics processing units (GPUs) are explained for the improvement of computation speed. The resulting GPU-PIC code executes aggregate time steps in two-dimensional geometry from 80 to 140 times faster than a conventional single CPU-PIC code with the same numerical scheme modelling a standard capacitively coupled plasma (CCP) reactor.