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Journal articles on the topic 'Lagrangian particle tracking'

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Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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1

Jones, Benjamin T., Andrew Solow, and Rubao Ji. "Resource Allocation for Lagrangian Tracking." Journal of Atmospheric and Oceanic Technology 33, no. 6 (June 2016): 1225–35. http://dx.doi.org/10.1175/jtech-d-15-0115.1.

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AbstractAccurate estimation of the transport probabilities among regions in the ocean provides valuable information for understanding plankton transport, the spread of pollutants, and the movement of water masses. Individual-based particle-tracking models simulate a large ensemble of Lagrangian particles and are a common method to estimate these transport probabilities. Simulating a large ensemble of Lagrangian particles is computationally expensive, and appropriately allocating resources can reduce the cost of this method. Two universal questions in the design of studies that use Lagrangian particle tracking are how many particles to release and how to distribute particle releases. A method is presented for tailoring the number and the release location of particles to most effectively achieve the objectives of a study. The method detailed here is a sequential analysis procedure that seeks to minimize the number of particles that are required to satisfy a predefined metric of result quality. The study assesses the result quality as the precision of the estimates for the elements of a transport matrix and also describes how the method may be extended for use with other metrics. Applying this methodology to both a theoretical system and a particle transport model of the Gulf of Maine results in more precise estimates of the transport probabilities with fewer particles than from uniformly or randomly distributing particle releases. The application of this method can help reduce the cost of and increase the robustness of results from studies that use Lagrangian particles.

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2

Zhao, Bin, Chun Chen, and Alvin C. K. Lai. "Lagrangian Stochastic Particle Tracking: Further Discussion." Aerosol Science and Technology 45, no. 8 (August 2011): 901–2. http://dx.doi.org/10.1080/02786826.2011.570382.

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3

Heus, Thijs, Gertjan van Dijk, Harm J. J. Jonker, and Harry E. A. Van den Akker. "Mixing in Shallow Cumulus Clouds Studied by Lagrangian Particle Tracking." Journal of the Atmospheric Sciences 65, no. 8 (August 1, 2008): 2581–97. http://dx.doi.org/10.1175/2008jas2572.1.

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Abstract Mixing between shallow cumulus clouds and their environment is studied using large-eddy simulations. The origin of in-cloud air is studied by two distinct methods: 1) by analyzing conserved variable mixing diagrams (Paluch diagrams) and 2) by tracing back cloud-air parcels represented by massless Lagrangian particles that follow the flow. The obtained Paluch diagrams are found to be similar to many results in the literature, but the source of entrained air found by particle tracking deviates from the source inferred from the Paluch analysis. Whereas the classical Paluch analysis seems to provide some evidence for cloud-top mixing, particle tracking shows that virtually all mixing occurs laterally. Particle trajectories averaged over the entire cloud ensemble also clearly indicate the absence of significant cloud-top mixing in shallow cumulus clouds.

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4

Shaffer, Franklin, Eric Ibarra, and Ömer Savaş. "Visualization of submerged turbulent jets using particle tracking velocimetry." Journal of Visualization 24, no. 4 (February 15, 2021): 699–710. http://dx.doi.org/10.1007/s12650-021-00744-4.

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Abstract Over the past few decades, advances have been made in using particle image velocimetry (PIV) and particle tracking velocimetry (PTV) for mapping of Lagrangian velocity and acceleration flow fields. With PIV, Lagrangian trajectories are not measured directly; rather, hypothetical trajectories must be constructed from sequences of Eulerian velocity snapshots. Because PTV directly measures actual trajectories, it provides distinct advantages over PIV, especially for trajectories with abrupt changes in direction. In this work, a novel particle tracking algorithm is described, then applied to track trajectories of tracer particles in submerged turbulent jets. The Reynolds numbers ranged from 1000 to 25,000, thereby covering laminar, transitioning-to-turbulence, and fully turbulent flow regimes. The novel particle tracking algorithm is designed to handle flows with very high particle concentrations, thereby resolving small-scale flow structures. Trajectories are tracked with high velocity gradients, sharp curvatures, cycloids, abrupt changes in direction, and strong recirculation—all of which are inaccessible via construction from PIV sequences. Most trajectories measured in this work are at least 500 camera frames (time steps) long, with many being more than 3000 frames long. Graphic abstract

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5

Kemp, L., Elizabeth C. Jamieson, and S. J. Gaskin. "Phosphorescent tracer particles for Lagrangian flow measurement and particle tracking velocimetry." Experiments in Fluids 48, no. 5 (January 20, 2010): 927–31. http://dx.doi.org/10.1007/s00348-009-0818-z.

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6

Tambasco, Mauro, and David A. Steinman. "On Assessing the Quality of Particle Tracking Through Computational Fluid Dynamic Models." Journal of Biomechanical Engineering 124, no. 2 (March 29, 2002): 166–75. http://dx.doi.org/10.1115/1.1449489.

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Quantification of particle deposition patterns, transit times, and shear exposure is important for computational fluid dynamic (CFD) studies involving respiratory and arterial models. To numerically compute such path-dependent quantities, it is necessary to employ a Lagrangian approach where particles are tracked through a pre-computed velocity field. However, it is difficult to determine in advance whether a particular velocity field is sufficiently resolved for the purposes of tracking particles accurately. Towards this end, we propose the use of volumetric residence time (VRT)—previously defined for 2-D studies of platelet activation and here extended to more physiologically relevant 3-D models—as a means of quantifying whether a volume of Lagrangian fluid elements (LFE’s) seeded uniformly and contiguously at the model inlet remains uniform throughout the flow domain. Such “Lagrangian mass conservation” is shown to be satisfied when VRT=1 throughout the model domain. To demonstrate this novel concept, we computed maps of VRT and particle deposition in 3-D steady flow models of a stenosed carotid bifurcation constructed with one adaptively refined and three nominally uniform finite element meshes of increasing element density. A key finding was that uniform VRT could not be achieved for even the most resolved meshes and densest LFE seeding, suggesting that care should be taken when extracting quantitative information about path-dependent quantities. The VRT maps were found to be useful for identifying regions of a mesh that were under-resolved for such Lagrangian studies, and for guiding the construction of more adequately resolved meshes.

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7

Nikolić, Srđan, Nenad Stevanović, and Miloš Ivanović. "Optimizing parallel particle tracking in Brownian motion using machine learning." International Journal of High Performance Computing Applications 34, no. 5 (June 25, 2020): 532–46. http://dx.doi.org/10.1177/1094342020936019.

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In this paper, we present a generic, scalable and adaptive load balancing parallel Lagrangian particle tracking approach in Wiener type processes such as Brownian motion. The approach is particularly suitable in problems involving particles with highly variable computation time, like deposition on boundaries that may include decay, when particle lifetime obeys exponential distribution. At first glance, Lagranginan tracking is highly suitable for a distributed programming model due to the independence of motion of separate particles. However, the commonly employed Decomposition Per Particle (DPP) method, where each process is in charge of a certain number of particles, actually displays poor parallel efficiency due to the high particle lifetime variability when dealing with a wide set of deposition problems that optionally include decay. The proposed method removes DPP defects and brings a novel approach to discrete particle tracking. The algorithm introduces master/slave model dubbed Partial Trajectory Decomposition (PTD), in which a certain number of processes produce partial trajectories and put them into the shared queue, while the remaining processes simulate actual particle motion using previously generated partial trajectories. Our approach also introduces meta-heuristics for determining the optimal values of partial trajectory length, chunk size and the number of processes acting as producers/consumers, for the given total number of participating processes (Optimized Partial Trajectory Decomposition, OPTD). The optimization process employs a surrogate model to estimate the simulation time. The surrogate is based on historical data and uses a coupled machine learning model, consisting of classification and regression phases. OPTD was implemented in C, using standard MPI for message passing and benchmarked on a model of 220 Rn progeny in the diffusion chamber, where particle motion is characterized by an exponential lifetime distribution and Maxwell velocity distribution. The speedup improvement of OPTD is approximatelly 320% over standard DPP, reaching almost ideal speedup on up to 256 CPUs.

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8

Arroyo-Chávez, Griselda, and Enrique Vázquez-Semadeni. "Evolution of the Angular Momentum during Gravitational Fragmentation of Molecular Clouds*." Astrophysical Journal 925, no. 1 (January 1, 2022): 78. http://dx.doi.org/10.3847/1538-4357/ac3915.

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Abstract We investigate the origin of the observed scaling j ∼ R 3/2 between the specific angular momentum j and the radius R of molecular clouds (MCs) and their their substructures, and of the observed near independence of β, the ratio of rotational to gravitational energy, from R. To this end, we measure the angular momentum (AM) of “Lagrangian” particle sets in a smoothed particle hydrodynamics (SPH) simulation of the formation, collapse, and fragmentation of giant MCs. The Lagrangian sets are initially defined as connected particle sets above a certain density threshold at a certain time t def, and then the same set of SPH particles is followed either forward or backward in time. We find the following. (i) The Lagrangian particle sets evolve along the observed j–R relation when the volume containing them also contains a large number of other “intruder” particles. Otherwise, they evolve with j ∼ cst. (ii) Tracking Lagrangian sets to the future, we find that a subset of the SPH particles participates in the collapse, while the rest disperses away. (iii) These results suggest that the Lagrangian sets of fluid particles exchange their AM with other neighboring fluid particles via turbulent viscosity. (iv) We conclude that the j–R relation arises from a global tendency toward gravitational contraction, mediated by AM loss via turbulent viscosity, which induces fragmentation into dense, low-AM clumps, and diffuse, high-AM envelopes, which disperse away, limiting the mass efficiency of the fragmentation.

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9

Chan, S. N., and J. H. W. Lee. "Particle tracking modeling of sediment-laden jets." Advances in Geosciences 39 (June 27, 2014): 107–14. http://dx.doi.org/10.5194/adgeo-39-107-2014.

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Abstract. This paper presents a general model to predict the particulate transport and deposition from a sediment-laden horizontal momentum jet. A three-dimensional (3-D) stochastic particle tracking model is developed based on the governing equation of particle motion. The turbulent velocity fluctuations are modelled by a Lagrangian velocity autocorrelation function that captures the trapping of sediment particles in turbulent eddies, which result in the reduction of settling velocity. Using classical solutions of mean jet velocity, and turbulent fluctuation and dissipation rate profiles derived from computational fluid dynamics calculations of a pure jet, the equation of motion is solved numerically to track the particle movement in the jet flow field. The 3-D particle tracking model predictions of sediment deposition and concentration profiles are in excellent agreement with measured data. The computationally demanding Basset history force is shown to be negligible in the prediction of bottom deposition profiles.

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10

Vennell, Ross, Max Scheel, Simon Weppe, Ben Knight, and Malcolm Smeaton. "Fast lagrangian particle tracking in unstructured ocean model grids." Ocean Dynamics 71, no. 4 (February 22, 2021): 423–37. http://dx.doi.org/10.1007/s10236-020-01436-7.

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11

Yang, Jin, Yue Yin, Alexander K. Landauer, Selda Buyukozturk, Jing Zhang, Luke Summey, Alexander McGhee, Matt K. Fu, John O. Dabiri, and Christian Franck. "SerialTrack: ScalE and rotation invariant augmented Lagrangian particle tracking." SoftwareX 19 (July 2022): 101204. http://dx.doi.org/10.1016/j.softx.2022.101204.

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12

Szwaykowska, Klementyna, and Fumin Zhang. "Controlled Lagrangian Particle Tracking: Error Growth Under Feedback Control." IEEE Transactions on Control Systems Technology 26, no. 3 (May 2018): 874–89. http://dx.doi.org/10.1109/tcst.2017.2695161.

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13

Narayanan, Chidambaram, Djamel Lakehal, and George Yadigaroglu. "Linear stability analysis of particle-laden mixing layers using Lagrangian particle tracking." Powder Technology 125, no. 2-3 (June 2002): 122–30. http://dx.doi.org/10.1016/s0032-5910(01)00498-3.

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14

van den Bremer, T. S., C. Whittaker, R. Calvert, A. Raby, and P. H. Taylor. "Experimental study of particle trajectories below deep-water surface gravity wave groups." Journal of Fluid Mechanics 879 (September 20, 2019): 168–86. http://dx.doi.org/10.1017/jfm.2019.584.

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Owing to the interplay between the forward Stokes drift and the backward wave-induced Eulerian return flow, Lagrangian particles underneath surface gravity wave groups can follow different trajectories depending on their initial depth below the surface. The motion of particles near the free surface is dominated by the waves and their Stokes drift, whereas particles at large depths follow horseshoe-shaped trajectories dominated by the Eulerian return flow. For unidirectional wave groups, a small net displacement in the direction of travel of the group results near the surface, and is accompanied by a net particle displacement in the opposite direction at depth. For deep-water waves, we study these trajectories experimentally by means of particle tracking velocimetry in a two-dimensional flume. In doing so, we provide visual illustration of Lagrangian trajectories under groups, including the contributions of both the Stokes drift and the Eulerian return flow to both the horizontal and the vertical Lagrangian displacements. We compare our experimental results to leading-order solutions of the irrotational water wave equations, finding good agreement.

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15

Francis Egenti, Nzerem, and Ugorji Hycinth Chimezie. "The Turbulent Lagrangian Dissipative Particle Velocity Statistics." Mediterranean Journal of Basic and Applied Sciences 06, no. 04 (2022): 84–92. http://dx.doi.org/10.46382/mjbas.2022.6408.

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A statistical description of turbulence comprising a probability distribution for stationary flows is the basis for determining the nature of turbulent velocity fluctuations. Away from the Eulerian spatial increments of the velocity field, the Lagrangian notion of temporal velocity increments along particle trajectories appears to be the hob of turbulent velocity statistics, ostensibly in the presence of inherent intermittencies observable in particle tracking. Such intermittencies were analyzed by using the well-known velocity structure functions, which defer to the Kolmogorov similarity theory (KST). Since particle trajectories, under normal circumstances, submit to Gaussian statistics, the deviations from Kolmogorov similarity theory are considered a culprit in the event of intermittency.

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16

Ding, Yu, Haifei Liu, and Wei Yang. "Numerical Prediction of the Short-Term Trajectory of Microplastic Particles in Laizhou Bay." Water 11, no. 11 (October 27, 2019): 2251. http://dx.doi.org/10.3390/w11112251.

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Microplastic particles are easily captured by microorganisms and enter the food chain, which poses a threat to ecological health. These particles are abundant in coastal areas because of the influence of anthropic activities and the interaction between the sea and land. Although much research on microplastics has been done, predicting the transportation of microplastic particles in coastal zones is still a challenge. In this paper, the trajectories of microplastic particles released from four river mouths around Laizhou Bay are investigated using the lattice Boltzmann method coupled with the Lagrangian particle-tracking method, involving inter-particle and particle-wall collisions. The trajectories of particles released from four river mouths are recorded within 30 days.

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17

Sciacchitano, Andrea, and Stefano Discetti. "Special issue on uncertainty quantification in particle image velocimetry and Lagrangian particle tracking." Measurement Science and Technology 33, no. 1 (October 20, 2021): 010201. http://dx.doi.org/10.1088/1361-6501/ac2c49.

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18

Siu, Y. W., and A. M. K. P. Taylor. "Particle capture by turbulent recirculation zones measured using long-time Lagrangian particle tracking." Experiments in Fluids 51, no. 1 (January 5, 2011): 95–121. http://dx.doi.org/10.1007/s00348-010-0913-1.

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19

Figueroa, Aldo, Sergio Cuevas, and Eduardo Ramos. "Lissajous trajectories in electromagnetically driven vortices." Journal of Fluid Mechanics 815 (February 21, 2017): 415–34. http://dx.doi.org/10.1017/jfm.2017.55.

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An experimental and theoretical study of laminar vortical flows driven by oscillating electromagnetic forces that act in orthogonal directions in a shallow electrolytic fluid layer is presented. Forces are generated by the interaction of the field of a dipolar permanent magnet and two imposed alternating electric currents perpendicular to each other with independent frequencies varying in the range of 10–30 mHz. Velocity fields of the time-dependent flow are obtained using particle image velocimetry, while particle tracking allows exploration of the Lagrangian trajectories and time maps. An approximate two-dimensional analytical solution is obtained for the laminar creeping regime so that Lagrangian trajectories are integrated explicitly. These trajectories resemble Lissajous figures with the usual property that, when the ratio of the frequencies of the imposed currents is rational, closed paths are found, while non-closed paths occur when this ratio is irrational. Deviations of this regime that account for slight increase of inertial effects are explored through a quasi-two-dimensional numerical simulation. In this case, non-closed paths are found even for rational frequency ratios. This case was observed in the experiment. Lagrangian trajectories calculated numerically show a qualitative agreement with experimental particle tracking. Furthermore, numerical time maps obtained for increasing inertial effects and rational frequency ratios reveal a chaotic behaviour. Some features of the Lagrangian trajectories are validated experimentally. In particular, topological properties of the calculated and observed time maps are in qualitative agreement. In a characteristic case, a partial time map calculated numerically is compared with the section acquired from the experimental tracking of one particle.

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20

Petrosino, F., D. De Rosa, and G. Mingione. "Application of different Lagrangian Particle Tracking techniques for water impingement." IOP Conference Series: Materials Science and Engineering 1024, no. 1 (January 1, 2021): 012011. http://dx.doi.org/10.1088/1757-899x/1024/1/012011.

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21

Wapperom, P., R. Keunings, and V. Legat. "The backward-tracking Lagrangian particle method for transient viscoelastic flows." Journal of Non-Newtonian Fluid Mechanics 91, no. 2-3 (July 2000): 273–95. http://dx.doi.org/10.1016/s0377-0257(99)00095-6.

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22

Ouellette, Nicholas T., Haitao Xu, and Eberhard Bodenschatz. "A quantitative study of three-dimensional Lagrangian particle tracking algorithms." Experiments in Fluids 40, no. 2 (November 15, 2005): 301–13. http://dx.doi.org/10.1007/s00348-005-0068-7.

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23

Dodds, David, Abd Alhamid R. Sarhan, and Jamal Naser. "CFD Investigation into the Effects of Surrounding Particle Location on the Drag Coefficient." Fluids 7, no. 10 (October 17, 2022): 331. http://dx.doi.org/10.3390/fluids7100331.

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In the simulation of dilute gas-solid flows such as those seen in many industrial applications, the Lagrangian Particle Tracking method is used to track packets of individual particles through a converged fluid field. In the tracking of these particles, the most dominant forces acting upon the particles are those of gravity and drag. In order to accurately predict particle motion, the determination of the aforementioned forces become of the upmost importance, and hence an improved drag force formula was developed to incorporate the effects of particle concentration and particle Reynolds number. The present CFD study examines the individual effects of particles located both perpendicular and parallel to the flow direction, as well as the effect of a particle entrain within an infinite matrix of evenly distributed particles. Results show that neighbouring particles perpendicular to the flow (Model 2) have an effect of increasing the drag force at close separation distances, but this becomes negligible between 5–10 particle diameters depending on particle Reynolds number (Rep). When entrained in an infinite line of particles co-aligned with the flow (Model 1), the drag force is remarkably reduced at close separation distances and increases as the distance increases. The results of the infinite matrix of particles (Model 3) show that, although not apparent in the individual model, the effect of side particles is experienced many particle diameters downstream.

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24

Onderik, Juraj, Michal Chládek, and Roman Ďurikovič. "Animating multiple interacting miscible and immiscible fluids based on particle simulation." Journal of Applied Mathematics, Statistics and Informatics 9, no. 2 (December 1, 2013): 73–86. http://dx.doi.org/10.2478/jamsi-2013-0014.

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Abstract We present a particle-based approach for animating multiple interacting liquids that can handle number of immiscible fluids as well as number of miscible fluids in our simulation framework. We solve the usual problem of robust interface tracking, between immiscible fluids, by reconstructing the zero level set of our novel composite implicit function, see Fig. 1 left and center. It’s recurrent formulation handles directly interfaces between any number of liquids including the free surfaces. We model the miscible fluids by tracking concentrations of dissolved materials in the vicinity of each particle. Flick’s law is applied for the Laplacian-based diffusion of concentrations, see Fig. 1 right. Particle sedimentation is achieved by directional advection along the settling velocity. The diffusion-advection equation is discretized by particles using the Lagrangian formulation. The proposed improvements can be easily implemented into the common Smoothed Particle Hydrodynamics (SPH) simulations framework

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25

Zreid, Imadeddin, Ronny Behnke, and Michael Kaliske. "ALE formulation for thermomechanical inelastic material models applied to tire forming and curing simulations." Computational Mechanics 67, no. 6 (April 24, 2021): 1543–57. http://dx.doi.org/10.1007/s00466-021-02005-5.

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AbstractForming of tires during production is a challenging process for Lagrangian solid mechanics due to large changes in the geometry and material properties of the rubber layers. This paper extends the Arbitrary Lagrangian–Eulerian (ALE) formulation to thermomechanical inelastic material models with special consideration of rubber. The ALE approach based on tracking the material and spatial meshes is used, and an operator-split is employed which splits up the solution within a time step into a mesh smoothing step, a history remapping step and a Lagrangian step. Mesh distortion is reduced in the smoothing step by solving a boundary value problem. History variables are subsequently remapped to the new mesh with a particle tracking scheme. Within the Lagrangian steps, a fully coupled thermomechanical problem is solved. An advanced two-phase rubber model is incorporated into the ALE approach, which can describe green rubber, cured rubber and the transition process. Several numerical examples demonstrate the superior behavior of the developed formulation in comparison to purely Lagrangian finite elements.

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26

Chung, Dang Huu, and Nguyen Thi Kieu Duyen. "Sensitivity of Lagrangian Particle Tracking Based on a 3D Numerical Model." Journal of Modern Physics 03, no. 12 (2012): 1972–78. http://dx.doi.org/10.4236/jmp.2012.312246.

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27

Szwaykowska, Klementyna, and Fumin Zhang. "Trend and Bounds for Error Growth in Controlled Lagrangian Particle Tracking." IEEE Journal of Oceanic Engineering 39, no. 1 (January 2014): 10–25. http://dx.doi.org/10.1109/joe.2012.2236491.

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Barker, Douglas, Jonathan Lifflander, Anshu Arya, and Yuanhui Zhang. "A parallel algorithm for 3D particle tracking and Lagrangian trajectory reconstruction." Measurement Science and Technology 23, no. 2 (December 16, 2011): 025301. http://dx.doi.org/10.1088/0957-0233/23/2/025301.

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29

Guo, Baoyu, David F. Fletcher, and Tim A. G. Langrish. "Simulation of the agglomeration in a spray using Lagrangian particle tracking." Applied Mathematical Modelling 28, no. 3 (March 2004): 273–90. http://dx.doi.org/10.1016/s0307-904x(03)00133-1.

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30

Bianco, F., S. Chibbaro, C. Marchioli, M. V. Salvetti, and A. Soldati. "Intrinsic filtering errors of Lagrangian particle tracking in LES flow fields." Physics of Fluids 24, no. 4 (April 2012): 045103. http://dx.doi.org/10.1063/1.3701378.

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31

Godbersen, Philipp, and Andreas Schröder. "Functional binning: improving convergence of Eulerian statistics from Lagrangian particle tracking." Measurement Science and Technology 31, no. 9 (June 25, 2020): 095304. http://dx.doi.org/10.1088/1361-6501/ab8b84.

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32

Badreddine, Hassan, Yohei Sato, Bojan Niceno, and Horst-Michael Prasser. "Finite size Lagrangian particle tracking approach to simulate dispersed bubbly flows." Chemical Engineering Science 122 (January 2015): 321–35. http://dx.doi.org/10.1016/j.ces.2014.09.037.

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Cheng, Y., and F. J. Diez. "A 4D imaging tool for Lagrangian particle tracking in stirred tanks." AIChE Journal 57, no. 8 (October 11, 2010): 1983–96. http://dx.doi.org/10.1002/aic.12429.

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Huilier, Daniel G. F. "An Overview of the Lagrangian Dispersion Modeling of Heavy Particles in Homogeneous Isotropic Turbulence and Considerations on Related LES Simulations." Fluids 6, no. 4 (April 8, 2021): 145. http://dx.doi.org/10.3390/fluids6040145.

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Particle tracking is a competitive technique widely used in two-phase flows and best suited to simulate the dispersion of heavy particles in the atmosphere. Most Lagrangian models in the statistical approach to turbulence are based either on the eddy interaction model (EIM) and the Monte-Carlo method or on random walk models (RWMs) making use of Markov chains and a Langevin equation. In the present work, both discontinuous and continuous random walk techniques are used to model the dispersion of heavy spherical particles in homogeneous isotropic stationary turbulence (HIST). Their efficiency to predict particle long time dispersion, mean-square velocity and Lagrangian integral time scales are discussed. Computation results with zero and no-zero mean drift velocity are reported; they are intended to quantify the inertia, gravity, crossing-trajectory and continuity effects controlling the dispersion. The calculations concern dense monodisperse spheres in air, the particle Stokes number ranging from 0.007 to 4. Due to the weaknesses of such models, a more sophisticated matrix method will also be explored, able to simulate the true fluid turbulence experienced by the particle for long time dispersion studies. Computer evolution and performance since allowed to develop, instead of Reynold-Averaged Navier-Stokes (RANS)-based studies, large eddy simulation (LES) and direct numerical simulation (DNS) of turbulence coupled to Generalized Langevin Models. A short review on the progress of the Lagrangian simulations based on large eddy simulation (LES) will therefore be provided too, highlighting preferential concentration. The theoretical framework for the fluid time correlation functions along the heavy particle path is that suggested by Wang and Stock.

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Zhang, Yong, HongGuang Sun, and Chunmiao Zheng. "Lagrangian solver for vector fractional diffusion in bounded anisotropic aquifers: Development and application." Fractional Calculus and Applied Analysis 22, no. 6 (December 18, 2019): 1607–40. http://dx.doi.org/10.1515/fca-2019-0083.

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Abstract Fractional-derivative models (FDMs) are promising tools for characterizing non-Fickian transport in natural geological media. Hydrologic applications of FDMs, however, have been limited in the last two decades, due to the lack of feasible models and solvers to quantify multi-dimensional anomalous diffusion for pollutants in bounded aquifers. This study develops and applies FDM tools to capture vector fractional dispersion for both conservative and reactive pollutants in fractional Brownian motion (fBm) random fields with bounded domains. A d-dimensional anisotropic fBm field for hydraulic conductivity (K) is first generated numerically. A particle-tracking based, fully Lagrangian solver is then developed to approximate particle dynamics in the fBm K fields under various boundary conditions, where the governing equation is the vector FDM subordination to regional flow. Numerical experiments show that the Lagrangian solver can combine nonlocal anomalous transport and local aquifer properties to quantify pollutant transport in bounded aquifers. Application analyses further reveal that the K correlation can significantly enhance the spreading of conservative pollutant particles, and increase the reaction rate by enhancing the mobility and mixing of reactant particles undergoing bimolecular reactions. Extension of the Lagrangian solver is also discussed, including modeling transient flow, generalizing boundary conditions, and capturing complex chemical reactions. This study therefore provides the hydrologic community an efficient Lagrangian solver to model reactive anomalous transport in bounded anisotropic aquifers with any dimension, size, and boundary conditions.

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Tomanovic, Ivan, Srdjan Belosevic, Aleksandar Milicevic, Nenad Crnomarkovic, and Dragan Tucakovic. "Numerical tracking of sorbent particles and distribution during gas desulfurization in pulverized coal-fired furnace." Thermal Science 21, suppl. 3 (2017): 759–69. http://dx.doi.org/10.2298/tsci160212196t.

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Furnace sorbent injection for sulfur removal from flue gas presents a challenge, as the proper process optimization is of crucial importance in order to obtain both high sulfur removal rates and good sorbent utilization. In the simulations a two-phase gas-particle flow is considered. Pulverized coal and calcium-based sorbent particles motion is simulated inside of the boiler furnace. It is important to determine trajectories of particles in the furnace, in order to monitor the particles heat and concentration history. A two-way coupling of the phases is considered ? influence of the gas phase on the particles, and vice versa. Particle-to-particle collisions are neglected. Mutual influence of gas and dispersed phase is modeled by corresponding terms in the transport equations for gas phase and the equations describing the particles turbulent dispersion. Gas phase is modeled in Eulerian field, while the particles are tracked in Lagrangian field. Turbulence is modeled by the standard k-? model, with additional terms for turbulence modulation. Distribution, dispersion and residence time of sorbent particles in the furnace have a considerable influence on the desulfurization process. It was shown that, by proper organization of process, significant improvement considering emission reduction can be achieved.

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Büyükçelebi, Banu Tansel, Hasan Karabay, and Ata Bilgili. "EXCHANGE CHARACTERISTICS OF AN ANTHROPOGENICALLY MODIFIED LAGOON: AN EULERIAN-LAGRANGIAN MODELING CASE STUDY WITH AN EMPHASIS ON THE NUMBER OF PARTICLES." Journal of Environmental Engineering and Landscape Management 29, no. 3 (August 23, 2021): 251–62. http://dx.doi.org/10.3846/jeelm.2021.15237.

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The transport pathways and exchange characteristics of the Kamil Abdüş Lagoon in Istanbul, Turkey, are simulated using a finite element model with a Lagrangian particle tracking module. The lagoon is in the process of being reconfigured. The simulations are performed using a draft configuration. The effect of winds and the number of particles on the e-folding time is simulated. Results show that the lagoon is strongly dominated by winds with a correlation coefficient of 0.897 between the wind and residual current magnitudes. The lagoon e-folds in 9.1 days under realistic winds and in 14.3 days when there is no wind with confidence levels of 5%. The Lagrangian study uses six simulations with particle numbers ranging between 65073 and 2730486. A methodology based on confidence levels is proposed. It is observed that approximately 784 000 particles are necessary to obtain 5% level of confidence. With a problematic history and new planning options, the lagoon has a potential to be used as an example setting, all-field study ground for anthropogenically engineered coastal ecosystems.

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Schauer, Lucas, Michael J. Schmidt, Nicholas B. Engdahl, Stephen D. Pankavich, David A. Benson, and Diogo Bolster. "Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes." Geoscientific Model Development 16, no. 3 (February 3, 2023): 833–49. http://dx.doi.org/10.5194/gmd-16-833-2023.

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Abstract. Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

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Li, Fu Sheng, Dong Sun, Xin Xi Xu, Xiu Guo Zhao, and Shu Lin Tan. "Numerical Simulation for Relationship between Vortex Evolution and Diffusion of Aerosol in Human Mouth-Throat Model." Advanced Materials Research 301-303 (July 2011): 456–61. http://dx.doi.org/10.4028/www.scientific.net/amr.301-303.456.

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The research on the relationship between vortex evolution and diffusion of aerosol in human upper respiratory tract can deepen understanding of the characteristics of the particle deposition pattern in human upper respiratory tract and plays a very important role in analyzing the transition of aerosol in human upper respiratory tract. Large eddy simulation and an efficient Lagrangian particle tracking module were used to simulate relationship between vortex evolution and diffusion of aerosol in mouth-throat model in the conditions of the low intensive respiratory, and the vortex evolution and the mechanism of aerosol transition in human mouth-throat model were discussed. The results show that the diffusion of small aerosol particles follow the vortex structure very closely; the capabilities of the vortex for carrying aerosol particle increase with increase in vorticity, which can affect the diffuseness and deposition of the particles.

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Wang, Bing, and Jing Lin. "Numerical prediction on deposition of micro-particulate matter in turbulent channel flows." International Journal of Modern Physics C 26, no. 12 (September 2015): 1550134. http://dx.doi.org/10.1142/s012918311550134x.

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A direct numerical simulation of Navier–Stokes equation coupled to the Lagrangian tracking of individual particles was used to predict the dispersion of deposited micro-particulate matter in turbulent channel flows on the walls. The different interaction conditions between particles and walls were considered for particles with Stokes numbers ranging from 0.1 to 104. The particle deposition rates were predicted accurately because of the accurate calculation of turbulence and particle dispersion. It was found the interaction between the turbulent particles and the walls determined the re-entrainment mechanism of inertial particles away from the wall. The dispersion of deposition of particles were independent of the wall conditions in the partial diffusional and whole diffusion-impaction regime, consistent with a log–log law with particle Stokes number, which was found to be [Formula: see text]. The deposition rate decreased with decreasing adhesion of the wall in the inertia-moderated regime. The present results may be helpful for establishing and evaluating accurate prediction models of micro-particle deposition rates in various engineering applications.

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Ross, Oliver N., and Jonathan Sharples. "Recipe for 1-D Lagrangian particle tracking models in space-varying diffusivity." Limnology and Oceanography: Methods 2, no. 9 (August 31, 2004): 289–302. http://dx.doi.org/10.4319/lom.2004.2.289.

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Ravnic, Dino J., Akira Tsuda, Aslihan Turhan, Juan P. Pratt, Harold T. Huss, Yu-Zhong Zhang, and Steven J. Mentzer. "Multiframe particle tracking in intravital imaging: defining Lagrangian coordinates in the microcirculation." BioTechniques 41, no. 5 (November 2006): 597–601. http://dx.doi.org/10.2144/000112262.

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Ravnik, Jure, Matjaz Hribersek, and Janez Lupse. "Lagrangian Particle Tracking in Velocity-Vorticity Resolved Viscous Flows by Subdomain BEM." Journal of Applied Fluid Mechanics 9, no. 3 (May 1, 2016): 1533–49. http://dx.doi.org/10.18869/acadpub.jafm.68.228.21590.

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Lu, Hao, Wen-Jun Zhao, Hui-Qiang Zhang, Bing Wang, and Xi-Lin Wang. "Particle transport behavior in air channel flow with multi-group Lagrangian tracking." Chinese Physics B 26, no. 1 (January 2017): 014702. http://dx.doi.org/10.1088/1674-1056/26/1/014702.

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Chibbaro, Sergio, Cristian Marchioli, Maria Vittoria Salvetti, and Alfredo Soldati. "Particle tracking in LES flow fields: conditional Lagrangian statistics of filtering error." Journal of Turbulence 15, no. 1 (January 2, 2014): 22–33. http://dx.doi.org/10.1080/14685248.2013.873541.

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Bensabat, Jacob, Quanlin Zhou, and Jacob Bear. "An adaptive pathline-based particle tracking algorithm for the Eulerian–Lagrangian method." Advances in Water Resources 23, no. 4 (January 2000): 383–97. http://dx.doi.org/10.1016/s0309-1708(99)00025-1.

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Fukushima, Naoya, Makito Katayama, Yoshitsugu Naka, Tsutomu Oobayashi, Masayasu Shimura, Yuzuru Nada, Mamoru Tanahashi, and Toshio Miyauchi. "Combustion regime classification of HCCI/PCCI combustion using Lagrangian fluid particle tracking." Proceedings of the Combustion Institute 35, no. 3 (2015): 3009–17. http://dx.doi.org/10.1016/j.proci.2014.07.059.

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Caraghiaur, Diana, and Henryk Anglart. "Drop deposition in annular two-phase flow calculated with Lagrangian Particle Tracking." Nuclear Engineering and Design 265 (December 2013): 856–66. http://dx.doi.org/10.1016/j.nucengdes.2013.06.026.

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Dunn, J. H., and S. G. Lambrakos. "Calculating Complex Interactions in Molecular Dynamics Simulations Employing Lagrangian Particle Tracking Schemes." Journal of Computational Physics 111, no. 1 (March 1994): 15–23. http://dx.doi.org/10.1006/jcph.1994.1039.

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Herrmann, M. "A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure." Journal of Computational Physics 229, no. 3 (February 2010): 745–59. http://dx.doi.org/10.1016/j.jcp.2009.10.009.

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