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1
Chakraborty, Rishiraj, Aaron Coutino und Marek Stastna. „Particle clustering and subclustering as a proxy for mixing in geophysical flows“. Nonlinear Processes in Geophysics 26, Nr. 3 (16.09.2019): 307–24. http://dx.doi.org/10.5194/npg-26-307-2019.
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Abstract. The Eulerian point of view is the traditional theoretical and numerical tool to describe fluid mechanics. Some modern computational fluid dynamics codes allow for the efficient simulation of particles, in turn facilitating a Lagrangian description of the flow. The existence and persistence of Lagrangian coherent structures in fluid flow has been a topic of considerable study. Here we focus on the ability of Lagrangian methods to characterize mixing in geophysical flows. We study the instability of a strongly non-linear double-jet flow, initially in geostrophic balance, which forms quasi-coherent vortices when subjected to ageostrophic perturbations. Particle clustering techniques are applied to study the behavior of the particles in the vicinity of coherent vortices. Changes in inter-particle distance play a key role in establishing the patterns in particle trajectories. This paper exploits graph theory in finding particle clusters and regions of dense interactions (also known as subclusters). The methods discussed and results presented in this paper can be used to identify mixing in a flow and extract information about particle behavior in coherent structures from a Lagrangian point of view.
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Rabczuk, T., T. Belytschko und S. P. Xiao. „Stable particle methods based on Lagrangian kernels“. Computer Methods in Applied Mechanics and Engineering 193, Nr. 12-14 (März 2004): 1035–63. http://dx.doi.org/10.1016/j.cma.2003.12.005.
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Healy, D. P., und J. B. Young. „Full Lagrangian methods for calculating particle concentration fields in dilute gas-particle flows“. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, Nr. 2059 (15.06.2005): 2197–225. http://dx.doi.org/10.1098/rspa.2004.1413.
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The paper discusses two Full Lagrangian methods for calculating the particle concentration and velocity fields in dilute gas-particle flows. The methods are mathematically similar but crucially different in application. By examining the analytical solution for two-phase stagnation-point flow, it is shown that Osiptsov's method is more general than that of Fernandez de la Mora and Rosner. In Osiptsov's method, the Jacobian of the Eulerian–Lagrangian transformation is computed by integration along particle pathlines. The particle concentration is then obtained algebraically from the Lagrangian form of the particle continuity equation. It is shown that the correct specification of the initial conditions is non-trivial and of vital importance. A technique to alleviate problems of mathematical ‘stiffness’ at small Stokes numbers is also described. Full Lagrangian methods require knowledge of the fluid velocity gradient field and, if the carrier flowfield is calculated numerically, differentiation of a ‘noisy’ field can result in serious errors. The paper describes a method for reducing these errors. The incompressible, inviscid flow over a cylinder provides a useful test case for validation and the Osiptsov method proves its worth by revealing a region, hitherto unknown, of crossing particle pathlines in the mathematical solution. Crossing pathlines and their relationship to Robinson's integral are then discussed, and calculations of particle flow through a turbine cascade at high Mach numbers are presented to illustrate the engineering potential of the method.
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Yan, Shiqiang, Q. W. Ma und Jinghua Wang. „Quadric SFDI for Laplacian Discretisation in Lagrangian Meshless Methods“. Journal of Marine Science and Application 19, Nr. 3 (September 2020): 362–80. http://dx.doi.org/10.1007/s11804-020-00159-x.
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Abstract In the Lagrangian meshless (particle) methods, such as the smoothed particle hydrodynamics (SPH), moving particle semi-implicit (MPS) method and meshless local Petrov-Galerkin method based on Rankine source solution (MLPG_R), the Laplacian discretisation is often required in order to solve the governing equations and/or estimate physical quantities (such as the viscous stresses). In some meshless applications, the Laplacians are also needed as stabilisation operators to enhance the pressure calculation. The particles in the Lagrangian methods move following the material velocity, yielding a disordered (random) particle distribution even though they may be distributed uniformly in the initial state. Different schemes have been developed for a direct estimation of second derivatives using finite difference, kernel integrations and weighted/moving least square method. Some of the schemes suffer from a poor convergent rate. Some have a better convergent rate but require inversions of high order matrices, yielding high computational costs. This paper presents a quadric semi-analytical finite-difference interpolation (QSFDI) scheme, which can achieve the same degree of the convergent rate as the best schemes available to date but requires the inversion of significant lower-order matrices, i.e. 3 × 3 for 3D cases, compared with 6 × 6 or 10 × 10 in the schemes with the best convergent rate. Systematic patch tests have been carried out for either estimating the Laplacian of given functions or solving Poisson’s equations. The convergence, accuracy and robustness of the present schemes are compared with the existing schemes. It will show that the present scheme requires considerably less computational time to achieve the same accuracy as the best schemes available in literatures, particularly for estimating the Laplacian of given functions.
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Oyinbo, Sunday Temitope, und Tien-Chien Jen. „Feasibility of numerical simulation methods on the Cold Gas Dynamic Spray (CGDS) Deposition process for ductile materials“. Manufacturing Review 7 (2020): 24. http://dx.doi.org/10.1051/mfreview/2020023.
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The techniques of cold gas dynamic spray (CGDS) coating involve the deposition of solid, high speed micron to nano particles onto a substrate. In contrast to a thermal spray, CGDS does not melt particles to retain their physico-chemical properties. There have been many advantages in developing microscopic analysis of deformation mechanisms with numerical simulation methods. Therefore, this study focuses on four cardinal numerical methods of analysis which are: Lagrangian, Smoothed Particles Hydrodynamics (SPH), Arbitrary Lagrangian-Eulerian (ALE), and Coupled Eulerian-Lagrangian (CEL) to examine the Cold Gas Dynamic Spray (CGDS) deposition system by simulating and analyzing the contact/impact problem at deformation zone using ductile materials. The details of these four numerical approaches are explained with some aspects of analysis procedure, model description, material model, boundary conditions, contact algorithm and mesh refinement. It can be observed that the material of the particle greatly influences the deposition and the deformation than the material of the substrate. Concerning the particle, a higher-density material such as Cu has a higher initial kinetic energy, which leads to a larger contact area, a longer contact time and, therefore, better bonding between the particle and the substrate. All the numerical methods studied, however, can be used to analyze the contact/impact problem at deformation zone during cold gas dynamic spray process.
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Campos Pinto, Martin, und Frédérique Charles. „From particle methods to forward-backward Lagrangian schemes“. SMAI journal of computational mathematics 4 (27.03.2018): 121–50. http://dx.doi.org/10.5802/smai-jcm.31.
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Nordam, Tor, Ruben Kristiansen, Raymond Nepstad, Erik van Sebille und Andy M. Booth. „A comparison of Eulerian and Lagrangian methods for vertical particle transport in the water column“. Geoscientific Model Development 16, Nr. 18 (19.09.2023): 5339–63. http://dx.doi.org/10.5194/gmd-16-5339-2023.
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Abstract. A common task in oceanography is to model the vertical movement of particles such as microplastics, nanoparticles, mineral particles, gas bubbles, oil droplets, fish eggs, plankton, or algae. In some cases, the distribution of the vertical rise or settling velocities of the particles in question can span a wide range, covering several orders of magnitude, often due to a broad particle size distribution or differences in density. This requires numerical methods that are able to adequately resolve a wide and possibly multi-modal velocity distribution. Lagrangian particle methods are commonly used for these applications. A strength of such methods is that each particle can have its own rise or settling speed, which makes it easy to achieve a good representation of a continuous distribution of speeds. An alternative approach is to use Eulerian methods, where the partial differential equations describing the transport problem are solved directly with numerical methods. In Eulerian methods, different rise or settling speeds must be represented as discrete classes, and in practice, only a limited number of classes can be included. Here, we consider three different examples of applications for a water column model: positively buoyant fish eggs, a mixture of positively and negatively buoyant microplastics, and positively buoyant oil droplets being entrained by waves. For each of the three cases, we formulate a model for the vertical transport based on the advection–diffusion equation with suitable boundary conditions and, in one case, a reaction term. We give a detailed description of an Eulerian and a Lagrangian implementation of these models, and we demonstrate that they give equivalent results for selected example cases. We also pay special attention to the convergence of the model results with an increasing number of classes in the Eulerian scheme and with the number of particles in the Lagrangian scheme. For the Lagrangian scheme, we see the 1/Np convergence, as expected for a Monte Carlo method, while for the Eulerian implementation, we see a second-order (1/Nk2) convergence with the number of classes.
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Wang, Yukun, Jingnan Sun, Meng Zhao, Alicia Murga, Sung-Jun Yoo, Kazuhide Ito und Zhengwei Long. „Numerical Study of Indoor Oil Mist Particle Concentration Distribution in an Industrial Factory Using the Eulerian–Eulerian and Eulerian–Lagrangian Methods“. Fluids 8, Nr. 10 (26.09.2023): 264. http://dx.doi.org/10.3390/fluids8100264.
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The transport and prediction of the concentration of particles in confined spaces are crucial for human well-being; this has become particularly evident during the current worldwide pandemic. Computational fluid dynamics (CFD) has been widely used for such predictions, relying on Eulerian–Eulerian (EE) and Eulerian–Lagrangian (EL) models to study particle flow. However, there is a lack of research on industrial factories. In this study, a scaled laboratory in an industrial factory was established for oil mist particles in a machining factory, and oil mist dispersion experiments were conducted under roof exhaust and mixed ventilation conditions. After that, the oil mist concentration distribution in the factory under the same working conditions was calculated by Eulerian and Lagrangian methods, and the corresponding calculation errors and resource consumption were compared. It was found that the simulation results of both methods are acceptable for mixed ventilation and roof exhaust ventilation systems. When there are more vortices in the factory, the Lagrangian method increases the computation time by more than 53% to satisfy the computational accuracy, and the computational error between the Eulerian and Lagrangian methods becomes about 10% larger. For oil mist particles with an aerodynamic diameter of 0.5 μm, both Eulerian and Lagrangian methods have reliable accuracy. Based on the same flow field, the Lagrangian method consumes more than 400 times more computational resources than the Eulerian method. This study can provide a reference for the simulation of indoor particulate transport in industrial factories.
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Floryan, J. M., und H. Rasmussen. „Numerical Methods for Viscous Flows With Moving Boundaries“. Applied Mechanics Reviews 42, Nr. 12 (01.12.1989): 323–41. http://dx.doi.org/10.1115/1.3152416.
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A review of numerical algorithms for the analysis of viscous flows with moving interfaces is presented. The review is supplemented with a discussion of methods that have been introduced in the context of other classes of free boundary problems, but which can be generalized to viscous flows with moving interfaces. The available algorithms can be classified as Eulerian, Lagrangian, and mixed, ie, Eulerian-Lagrangian. Eulerian algorithms consist of fixed grid methods, adaptive grid methods, mapping methods, and special methods. Lagrangian algorithms consist of strictly Lagrangian methods, Lagrangian methods with rezoning, free Lagrangian methods and particle methods. Mixed methods rely on both Lagrangian and Eulerian concepts. The review consists of a description of the present state-of-the-art of each group of algorithms and their applications to a variety of problems. The existing methods are effective in dealing with small to medium interface deformations. For problems with medium to large deformations the methods produce results that are reasonable from a physical viewpoint; however, their accuracy is difficult to ascertain.
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Davis, Sean L., Gustaaf B. Jacobs, Oishik Sen und H. S. Udaykumar. „SPARSE—A subgrid particle averaged Reynolds stress equivalent model: testing with a priori closure“. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, Nr. 2199 (März 2017): 20160769. http://dx.doi.org/10.1098/rspa.2016.0769.
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A Lagrangian particle cloud model is proposed that accounts for the effects of Reynolds-averaged particle and turbulent stresses and the averaged carrier-phase velocity of the subparticle cloud scale on the averaged motion and velocity of the cloud. The SPARSE (subgrid particle averaged Reynolds stress equivalent) model is based on a combination of a truncated Taylor expansion of a drag correction function and Reynolds averaging. It reduces the required number of computational parcels to trace a cloud of particles in Eulerian–Lagrangian methods for the simulation of particle-laden flow. Closure is performed in an a priori manner using a reference simulation where all particles in the cloud are traced individually with a point-particle model. Comparison of a first-order model and SPARSE with the reference simulation in one dimension shows that both the stress and the averaging of the carrier-phase velocity on the cloud subscale affect the averaged motion of the particle. A three-dimensional isotropic turbulence computation shows that only one computational parcel is sufficient to accurately trace a cloud of tens of thousands of particles.
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Gaugele, T., F. Fleissner und P. Eberhard. „Simulation of material tests using meshfree Lagrangian particle methods“. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 222, Nr. 4 (Dezember 2008): 327–38. http://dx.doi.org/10.1243/14644193jmbd167.
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Rutherford, B., und M. T. Montgomery. „A Lagrangian analysis of a developing and non-developing disturbance observed during the PREDICT experiment“. Atmospheric Chemistry and Physics Discussions 11, Nr. 12 (19.12.2011): 33273–323. http://dx.doi.org/10.5194/acpd-11-33273-2011.
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Abstract. The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of new Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation. Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed objectively. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance. The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics developed here are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.
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Ricker, Marcel, und Emil V. Stanev. „Circulation of the European northwest shelf: a Lagrangian perspective“. Ocean Science 16, Nr. 3 (25.05.2020): 637–55. http://dx.doi.org/10.5194/os-16-637-2020.
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Abstract. The dynamics of the European northwest shelf (ENWS), the surrounding deep ocean, and the continental slope between them are analysed in a framework of numerical simulations using Lagrangian methods. Several sensitivity experiments are carried out in which (1) the tides are switched off, (2) the wind forcing is low-pass filtered, and (3) the wind forcing is switched off. To measure accumulation of neutrally buoyant particles, a quantity named the “normalised cumulative particle density (NCPD)” is introduced. Yearly averages of monthly results in the deep ocean show no permanent particle accumulation areas at the surface. On the shelf, elongated accumulation patterns persist in yearly averages, often occurring along the thermohaline fronts. In contrast, monthly accumulation patterns are highly variable in both regimes. Tides substantially affect the particle dynamics on the shelf and thus the positions of fronts. The contribution of wind variability to particle accumulation in specific regions is comparable to that of tides. The role of vertical velocities in the dynamics of Lagrangian particles is quantified for both the eddy-dominated deep ocean and for the shallow shelf. In the latter area, winds normal to coasts result in upwelling and downwelling, illustrating the importance of vertical dynamics in shelf seas. Clear patterns characterising the accumulation of Lagrangian particles are associated with the vertical circulations.
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Namazian, Z., A. F. Najafi und S. M. Mousavian. „Numerical Simulation of Particle-Gas Flow Through a Fixed Pipe, Using One-Way and Two-Way Coupling Methods“. Journal of Mechanics 33, Nr. 2 (15.07.2016): 205–12. http://dx.doi.org/10.1017/jmech.2016.53.
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AbstractA numerical simulation of the particle-gas flow in a vertical turbulent pipe flow was conducted. The main objective of the present article is to investigate the effects of dispersed phase (particles) on continuous phase (gas). In so doing, two general forms of Eulerian-Lagrangian approaches namely, one-way (when the fluid flow is not affected by the presence of the particles) and two-way (when the particles exert a feedback force on the fluid) couplings were used to describe the equations of motion of the two-phase flow. Gas-phase velocities which are within the order of magnitude as that of particles, volume fraction, and particle Stokes number were calculated and the results were subsequently compared with the available experimental data. The simulated results show that when the particles are added, the fluid velocity is attenuated. With an increase in particle volume fraction, particle mass loading and Stokes number, velocity attenuation also increases. Moreover, the results indicate that an increase in particle Stokes number reduces the special limited particle volume fraction, according to which one-way coupling method yields plausible results. The results have also indicated that the significance of particle fluid interaction is not merely a function of volume fraction and particle Stokes number.
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Colagrossi, Andrea, Emanuele Rossi, Salvatore Marrone und David Le Touzé. „Particle Methods for Viscous Flows: Analogies and Differences Between the SPH and DVH Methods“. Communications in Computational Physics 20, Nr. 3 (31.08.2016): 660–88. http://dx.doi.org/10.4208/cicp.150915.170316a.
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AbstractIn this work two particle methods are studied in the context of viscous flows. The first one is a Vortex Particle Method, called Diffused Vortex Hydrodynamics (DVH), recently developed to simulate complex viscous flows at medium and high Reynolds regimes. This method presents some similarities with the SPH model and its Lagrangian meshless nature, even if it is based on a different numerical approach. Advantages and drawbacks of the two methods have been previously studied in Colagrossi et al. [1] from a theoretical point of view and in Rossi et al. [2], where these particle methods have been tested on selected benchmarks. Further investigations are presented in this article highlighting analogies and differences between the two particle models.
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Rutherford, B., und M. T. Montgomery. „A Lagrangian analysis of a developing and non-developing disturbance observed during the PREDICT experiment“. Atmospheric Chemistry and Physics 12, Nr. 23 (03.12.2012): 11355–81. http://dx.doi.org/10.5194/acp-12-11355-2012.
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Abstract. The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation. Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance. The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.
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Cottet, Georges-Henri. „Semi-Lagrangian particle methods for high-dimensional Vlasov–Poisson systems“. Journal of Computational Physics 365 (Juli 2018): 362–75. http://dx.doi.org/10.1016/j.jcp.2018.03.042.
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Eberhard, Peter, und Timo Gaugele. „Simulation of cutting processes using mesh-free Lagrangian particle methods“. Computational Mechanics 51, Nr. 3 (26.05.2012): 261–78. http://dx.doi.org/10.1007/s00466-012-0720-z.
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Chiswell, Stephen M. „Lagrangian Time Scales and Eddy Diffusivity at 1000 m Compared to the Surface in the South Pacific and Indian Oceans“. Journal of Physical Oceanography 43, Nr. 12 (01.12.2013): 2718–32. http://dx.doi.org/10.1175/jpo-d-13-044.1.
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Abstract Argo floats cannot be regarded as true Lagrangian drifters because they periodically rise to the surface. Hence, previous estimates of eddy diffusivity at depth using single-particle statistics have been limited to one submerged cycle. However, unless the Lagrangian time scale is significantly shorter than the Argo cycle time, this single-particle calculation can have a large bias. Here, eddy diffusivity computed from single-particle statistics using Argo data is compared to that computed by assuming that Eulerian scales at depth are the same as at the surface, and that the relationship between Lagrangian and Eulerian time scales derived by Middleton is valid. If the methods provide the same answer, one can have confidence in both methods. Eddy diffusivity calculated from the single-particle statistics shows the same spatial structure as that computed from inferred time scale, but is smaller by a factor of about 2. It is suggested that this is because the deep Lagrangian time scale over much of the region is comparable to, or longer than, the 10-day Argo submergence cycle.
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Heus, Thijs, Gertjan van Dijk, Harm J. J. Jonker und Harry E. A. Van den Akker. „Mixing in Shallow Cumulus Clouds Studied by Lagrangian Particle Tracking“. Journal of the Atmospheric Sciences 65, Nr. 8 (01.08.2008): 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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Lu, Shengfang, Weijian Chen, Dalin Zhang, Zihao Zhang und Guangya Zhu. „Investigation on Phase Transition and Collection Characteristics of Non-Spherical Ice Crystals with Eulerian and Lagrangian Methods“. Aerospace 11, Nr. 4 (11.04.2024): 299. http://dx.doi.org/10.3390/aerospace11040299.
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Ice crystal icing occurs in jet engine compressors, which can severely degrade jet engine performance. In this paper, two different numerical calculation methods, the Eulerian method and the Lagrangian method, were used to evaluate the dynamics, mass transfer, heat transfer, phase transition and trajectory of ice crystals. Then, we studied the effects of initial diameter, initial sphericity, initial temperature of ice crystal, and relative humidity of airflow on the phase transition and collection characteristics of ice crystal particles. Results indicate that the non-spherical characteristics of ice crystals have a significant impact on their impingement limits and collection characteristics. The collection coefficient of unmelted ice crystals is positively correlated with the initial particle diameter and sphericity, and negatively correlated with the initial particle temperature and the relative humidity of airflow. The melting rate of ice crystal particles on the impact surface increases exponentially with the initial diameter of the particles, linearly increases with the relative humidity of the airflow and initial temperature of the particles, and exponentially decreases with the sphericity of the particles.
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OSTAD, H., und S. MOHAMMADI. „A STABILIZED PARTICLE METHOD FOR LARGE DEFORMATION DYNAMIC ANALYSIS OF STRUCTURES“. International Journal of Structural Stability and Dynamics 12, Nr. 04 (Juli 2012): 1250026. http://dx.doi.org/10.1142/s0219455412500265.
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The property of free movement of particles allows for most meshless particle methods to be efficiently used for simulation of solid problems involving large deformation as it removes the necessity of remeshing, which is one of the time-consuming parts of the traditional finite element method based on an updated Lagrangian formulation. One of the main sources of instabilities in meshfree particle methods, which approximate the strong form of partial differential equations, is the existence of extra high frequency vibrations. They are induced into the solution due to the use of truncated Taylor series expansions. The cumulative effect of the extra vibrations makes the solution to be polluted by zero energy modes and tensile instabilities. In this paper, the CSPM particle method is used to solve elastodynamic large deformation problems based on an updated Lagrangian procedure. A field smoothing approach, recently proposed for reduction of instabilities that rise from excessive high frequency vibrations, is further extended to large deformation problems. Also, the phenomenon of particles penetration can be prevented without the requirement of any additional artificial damping forces. Another major advantage of the new approach is its generality which allows for its implementation into other particle methods and its application for solving other physical problems. A variety of large deformation problems are solved by the proposed approach and the results are compared with other available results.
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Глазунов, А. В. „Numerical simulation of turbulence and transport of fine particulate impurities in street canyons“. Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), Nr. 1(55) (13.03.2018): 17–37. http://dx.doi.org/10.26089/nummet.v19r103.
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При помощи LES-модели, содержащей блок лагранжева переноса частиц, проведены расчеты турбулентности и распространения мелкодисперсных примесей в городской среде. Рассматривалась упрощенная геометрия периодической последовательности городских каньонов при поперечном направлении среднего ветра. Проведено тестирование различных лагранжевых методов и их сравнение с эйлеровыми методами переноса концентрации примесей, а также сравнение результатов расчетов с лабораторными данными. Выполнены расчеты переноса тяжелых углеродных частиц с размерами до семидесяти микрон в диаметре. На основе анализа лагранжевых траекторий частиц выявлены закономерности переноса мелкодисперсной примеси турбулентностью и крупными вихрями. The LES-model combined with the Lagrangian particle transport procedure is used to simulate the turbulence and propagation of particulate impurities in urban environment. A simplified geometry for a periodic sequence of urban canyons is considered in the case of the transverse mean wind direction. A number of the Lagrangian methods are tested and compared with the Eulerian methods of scalar concentration transport. The obtained numerical results are also compared with experimental data. The transport of heavy carbon particles up to seventy microns in diameter is numerically studied. The regularities in the impurity transport by the turbulence and large eddies are revealed on the basis of the analysis of Lagrangian particle trajectories.
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Ryatina, E., und A. Lagno. „The Barnes — Hut-type algorithm in 2D Lagrangian vortex particle methods“. Journal of Physics: Conference Series 1715 (Januar 2021): 012069. http://dx.doi.org/10.1088/1742-6596/1715/1/012069.
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Lei, Yan, Xiaojie Liang, Dingwu Zhou, Tao Qiu, Kaixin Wang und Yue Wu. „Effect of Particle Diameter on Primary Breakup of High-Pressure Diesel Spray Atomization: A Study Based on Numerical Simulations Using the Eulerian–Lagrangian Model“. Energies 16, Nr. 1 (26.12.2022): 238. http://dx.doi.org/10.3390/en16010238.
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The coupling of Eulerian and Lagrangian methods in the Eulerian–Lagrangian Spray Atomization (ELSA) approach is critical. This study proposes an equation for the primary breakup particle diameter D of a diesel fuel spray and adopts it as a key transition criterion for coupling. A three-dimensional diesel spray is modeled by the large-eddy simulation (LES) approach. This improved ELSA simulation was conducted using various transition criteria for particle diameter Dcr. The results show that fuel spray experiences two stages: stage I, when a liquid column appears without a dispersed phase, and stage II, when primary breakup occurs with many discrete particles. Although Dcr has little influence on the macro-spray characteristics, such as top penetration distance S and spray cone angle θ, it has significant effects on discrete particles, such as their number, average diameter, distribution and location, and spray cone area. Dcr should be determined on the basis of actual operating conditions.
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Zheligovsky, Vladislav, und Uriel Frisch. „Time-analyticity of Lagrangian particle trajectories in ideal fluid flow“. Journal of Fluid Mechanics 749 (16.05.2014): 404–30. http://dx.doi.org/10.1017/jfm.2014.221.
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AbstractIt is known that the Eulerian and Lagrangian structures of fluid flow can be drastically different; for example, ideal fluid flow can have a trivial (static) Eulerian structure, while displaying chaotic streamlines. Here, we show that ideal flow with limited spatial smoothness (an initial vorticity that is just a little better than continuous) nevertheless has time-analytic Lagrangian trajectories before the initial limited smoothness is lost. To prove these results we use a little-known Lagrangian formulation of ideal fluid flow derived by Cauchy in 1815 in a manuscript submitted for a prize of the French Academy. This formulation leads to simple recurrence relations among the time-Taylor coefficients of the Lagrangian map from initial to current fluid particle positions; the coefficients can then be bounded using elementary methods. We first consider various classes of incompressible fluid flow, governed by the Euler equations, and then turn to highly compressible flow, governed by the Euler–Poisson equations, a case of cosmological relevance. The recurrence relations associated with the Lagrangian formulation of these incompressible and compressible problems are so closely related that the proofs of time-analyticity are basically identical.
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Pérez-Muñuzuri, Vicente, Jorge Eiras-Barca und Daniel Garaboa-Paz. „Tagging moisture sources with Lagrangian and inertial tracers: application to intense atmospheric river events“. Earth System Dynamics 9, Nr. 2 (08.06.2018): 785–95. http://dx.doi.org/10.5194/esd-9-785-2018.
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Abstract. Two Lagrangian tracer tools are evaluated for studies on atmospheric moisture sources and pathways. In these methods, a moisture volume is assigned to each particle, which is then advected by the wind flow. Usual Lagrangian methods consider this volume to remain constant and the particle to follow flow path lines exactly. In a different approach, the initial moisture volume can be considered to depend on time as it is advected by the flow due to thermodynamic processes. In this case, the tracer volume drag must be taken into account. Equations have been implemented and moisture convection was taken into account for both Lagrangian and inertial models. We apply these methods to evaluate the intense atmospheric rivers that devastated (i) the Pacific Northwest region of the US and (ii) the western Iberian Peninsula with flooding rains and intense winds in early November 2006 and 20 May 1994, respectively. We note that the usual Lagrangian method underestimates moisture availability in the continent, while active tracers achieve more realistic results.
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Bisyk, S. P., I. B. Chepkov, M. I. Vaskivskyi, L. S. Davydovskyi, O. A. Slуvinskуi und O. M. Aristarkhov. „Methods for modelling Air blast on structures in LS-DYNA. Comparison and analysys“. Озброєння та військова техніка 21, Nr. 1 (26.03.2019): 22–31. http://dx.doi.org/10.34169/2414-0651.2019.1(21).22-31.
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The results of modeling the effect of an explosion on a metal plate using different calculation methods are presented: LOAD_BLAST; LOAD_BLAST_ENHANCED; Arbitrary Lagrangian Eulerian; Particle Blast Method; Smooth Particle Hydrodynamics, implemented in the LS-DYNA program. The adequacy and accuracy of these methods is estimated, depending on the distance factor to the explosive. Bringing the advantages and disadvantages of each method and recommendations for their application based on the results of this simulation and the experience of the authors.
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Wu, C. T., W. Hu und M. Koishi. „A Smoothed Particle Galerkin Formulation for Extreme Material Flow Analysis in Bulk Forming Applications“. International Journal of Computational Methods 13, Nr. 03 (31.05.2016): 1650019. http://dx.doi.org/10.1142/s0219876216500195.
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This paper presents a new particle formulation for extreme material flow analyses in the bulk forming applications. The new formulation is first established by an introduction of a smoothed displacement field to the standard Galerkin formulation to eliminate zero-energy modes in conventional particle methods. The discretized system of linear equations is consistently derived and integrated using a direct nodal integration scheme. The linear formulation is next extended to the large deformation quasi-static analysis of inelastic materials. As quasi-static Lagrangian simulation proceeds in the severe deformation range, the analysis method is switched to explicit dynamics formulation and an adaptive Lagrangian kernel approach is preformed to reset the reference configuration and maintain the injective deformation mapping at the particles. Both nonconvex and convex meshfree approximations are investigated in this study. Several numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed method.
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Gai, Guodong, Olivier Thomine, Abdellah Hadjadj, Sergey Kudriakov und Anthony Wachs. „Preferential Concentration of Particles in Forced Turbulent Flows: Effects of Gravity“. Energies 16, Nr. 6 (22.03.2023): 2910. http://dx.doi.org/10.3390/en16062910.
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The impact of gravity on the particle preferential concentration is investigated by direct numerical simulations in an Eulerian–Lagrangian framework for a large range of Stokes numbers Stη=0.01∼4. For particles with small Stokes numbers such as Stη=0.01, the gravity has minor effects on the particle spatial distribution in the turbulence. With increasing Stη, stripped structures of the high number density of particles appear and expand along the gravity direction. Different evaluation methods of particle preferential concentration are discussed such as the spatial distribution, the box index, and the probability density function. The number density of particles in the accumulating regions reduced under the influence of gravity. The reduction becomes prominent for the particle cloud at Stokes number Stη≈1, especially in the clusters of high particle number density. For large Stokes number Stη, the slip velocity significantly increases due to the particle gravity. Due to the gravity, the particle concentration reduces globally, particularly in the low vorticity regions. For the Stokes number range explored in this paper, gravity has a considerable impact on the particle-turbulence interaction.
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Gilfanov, A. K., T. S. Zaripov, S. S. Sazhin und O. Rybdylova. „The Analysis of Particle Number Densities in Dilute Gas-Particle Flows: The Eulerian and Lagrangian Methods“. Lobachevskii Journal of Mathematics 43, Nr. 10 (Oktober 2022): 2938–47. http://dx.doi.org/10.1134/s1995080222130145.
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HUANG, RONGPEI, und CAISHENG LIAO. „GEOMETRICAL PARTICLE MODELS ON 3D LIGHTLIKE CURVES“. Modern Physics Letters A 21, Nr. 40 (28.12.2006): 3039–48. http://dx.doi.org/10.1142/s0217732306020603.
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The (2+1)-dimensional mechanical systems associated with lightlike curves are considered. We studied the action whose Lagrangian depends quadratically on the Cartan curvature (torsion). Some conservation laws are given and the motion equation for a special case is completely solved by using geometrical methods.
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Marri, Mahendher, und Dr Rehan Ahmed. „Impact Mechanics of Thin Metal Plates Using Lagrangian, CEL and SPH Methods“. International Journal of Engineering and Advanced Technology 13, Nr. 6 (30.08.2024): 22–36. http://dx.doi.org/10.35940/ijeat.f4528.13060824.
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This paper aimed to evaluate the ballistic limit for high-speed perpendicular and oblique impacts on thin aluminium alloy (AA6061-T651, Al5052) plates. Finite Element Analysis (FEA) was conducted on a commercially available software, Abaqus/Explicit®. The impact velocities in the model ranged from 100 m/s to 1000 m/s. Three distinctive modelling techniques were compared for simulating high-speed impacts, i.e., Smoothed Particle Hydrodynamics (SPH), Coupled Eulerian and Lagrangian (CEL) and Lagrangian. This investigation considered two different projectile shapes, i.e., conical and blunt. Plate thickness varied as 16, 20, and 26.3mm using the Lagrangian analysis. The influence of the physical properties of projectiles was analysed by comparing deformable and analytically rigid projectiles. The results of this study showed a good agreement with published data (experimental and FEA) for the Lagrangian model for both perpendicular and oblique impacts. The CEL method overestimated the ballistic limit, whereas the SPH model slightly underestimated the ballistic limit. The accuracy of the SPH model was velocity dependent, with a % error ranging from 3% (higher velocity) to 21% (lower velocity). The CEL model also showed velocity-dependent accuracy. The CEL model showed the highest percentage of energy absorption during contact interaction at the ballistic limit for perpendicular conical impacts. In contrast, Lagrangian and SPH models showed very similar energy absorption results for the blunt projectiles regardless of the impact angle. Changing the deformable projectile to analytical rigid varied the velocity-dependent % error from 2 to 38%.
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Johnson, Gordon R. „Linking of Lagrangian particle methods to standard finite element methods for high velocity impact computations“. Nuclear Engineering and Design 150, Nr. 2-3 (September 1994): 265–74. http://dx.doi.org/10.1016/0029-5493(94)90143-0.
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Rautenbach, Ryan, Sebastian Hofmann, Lukas Buntkiel, Jan Schäfer, Sebastian Felix Reinecke, Marko Hoffmann, Uwe Hampel und Michael Schlüter. „Dynamics of Lagrangian Sensor Particles: The Effect of Non-Homogeneous Mass Distribution“. Processes 12, Nr. 8 (01.08.2024): 1617. http://dx.doi.org/10.3390/pr12081617.
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The growing demand for bio-pharmaceuticals necessitates improved methods for the characterization of stirred tank reactors (STRs) and their mixing heterogeneities. Traditional Eulerian measurement approaches fall short, culminating in the use of Lagrangian Sensor Particles (LSPs) to map large-scale STRs and track the lifelines of microorganisms such as Chinese Hamster Ovary cells. This study investigates the hydrodynamic characteristics of LSPs, specifically examining the effects that the size and position of the Center of Mass (CoM) have on their flow-following capabilities. Two Lagrangian Particle (LP) designs are evaluated, one with the CoM and a Geometric Center aligned, and another with a shifted CoM. The experimental study is conducted in a rectangular vessel filled with deionized water featuring a stationary circular flow. Off-center LPs exhibit higher velocities, an increased number of floor contacts, and moreover, a less homogeneous particle probability of presence within the vessel compared to LPs with CoM and Geometric Center aligned. Lattice Boltzmann Large Eddy Simulations provide complementary undisturbed fluid velocity data for the calculation of the Stokes number St. Building upon these findings, differences in the Stokes number St between the two LP variants of ΔSt = 0.01 (25 mm LP) and ΔSt = 0.13 (40 mm LP) are calculated, highlighting the difference in flow behavior. Furthermore, this study offers a more representative calculation of particle response time approach, as the traditional Stokes number definition does not account for non-homogeneous particles, resulting in an alternative Stokes number (ΔStalt = 0.84 (25 mm LP) and ΔStalt = 2.72 (40 mm LP)). This study contributes to the improved characterization of STRs through the use of Lagrangian Sensor Particles. Results highlight the implications the internal mass distribution has on LSP design, offering crucial considerations for researchers in the field.
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Schanz, D., T. Jahn und A. Schröder. „3D Particle Position Determination And Correction At High Particle Densities“. Proceedings of the International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics 20 (11.07.2022): 1–17. http://dx.doi.org/10.55037/lxlaser.20th.214.
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The method of Iterative Particle Reconstruction (IPR), introduced by Wieneke in 2013, constitutes a major step towards high-density 3D Lagrangian Particle Tracking. It reconstructs 3D particle positions from their projections onto several cameras. In the first part of this work, we present several approaches to enhance the original IPR working principle which, in combination, nearly triple the processable particle image densities, allowing complete and ghost-free reconstructions on a single snapshot from a four-camera system at up to 0.14 particles-per pixel (ppp). The updated method is proven to be fast, accurate and robust against image noise and other imaging artifacts. A central piece of the IPR functionality is a position optimization algorithm, using the difference of the local re-projected and original images (the residual images) as a cost function and displacing particles along its steepest gradient ('shaking' of the particles). The same approach is used within the Shake-The-Box (STB) Lagrangian Particle Tracking (LPT) scheme to correct predicted particle positions. The positional errors to be corrected during IPR-processing are typically in the sub-pixel range, however larger errors can occur at the prediction stage of STB. The second part of this manuscript quantifies the ability of the position optimization to successfully correct misplaced particles and proposes a method to further increase this range. Cost-function-gradient based methods require a certain overlap of the re-projected image with the original image for any given particle. Still, a misplacement of 2-3 pixels - depending on its direction relative to the camera positions - is shown to be reliably correctable. As seen by statistics from a DNS of a turbulent cylinder flow, such high accelerations (and therefore mispredictions) are rare at typical sampling rates. Therefore, most particle predictions can be successfully optimized to the correct position. In order to additionally handle rare events of large acceleration and misplacement, an iterative grid-search is applied specifically to particles not being optimally placed yet ('Variable Space step', VS). Such particles are identified using the local shape of the cost-function gradient. Using synthetic data, it is demonstrated that this method is able to correct even large prediction errors with high reliability. Applying a low temporal sampling on the test case of turbulent cylinder flow results in 20.8 px average particle shift. In this case, using noisy image data at a particle image density of 0.1 ppp, approx. 95.3% of the particle predictions can be corrected by pure position optimization, while around 99.5 % are achieved by additionally applying VS. Transferring this approach to experimental data could further improve tracking fidelity and would allow relaxing on the temporal resolution demands.
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Zhou, Ke, Samuel Jacobi Grauer, Daniel Schanz, Philipp Godbersen, Andreas Schröder, Thomas Rockstroh, Young Jin Jeon und Bernhard Wieneke. „Benchmarking Data Assimilation Algorithms For 3D Lagrangian Particle Tracking“. Proceedings of the International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics 21 (08.07.2024): 1–22. http://dx.doi.org/10.55037/lxlaser.21st.229.
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This paper reports a comparison of three state-of-the-art data assimilation (DA) algorithms for 3D Lagrangian particle tracking (LPT): Vortex-In-Cell sharp (VIC#), FlowFit3, and neural-implicit particle advection (NIPA). Particle trajectories, termed “tracks,” are spatially sparse, and a reconstruction algorithm is commonly employed to estimate dense Eulerian fields using position, velocity, and/or acceleration data from the tracks. DA algorithms for LPT combine the tracks with a set of governing equations (or constraints) to enhance the accuracy of the velocity field, relative to interpolation methods, and infer additional quantities like pressure. We compare the performance of VIC#, FlowFit3, and NIPA with respect to their accuracy and computational cost. Accuracy is assessed in terms of the mean inter-particle distance, frame rate, and magnitude of tracking errors, and costs are reported in wall time. Synthetic and experimental data sets for homogeneous isotropic turbulence and turbulent boundary layer flows are evaluated; direct numerical simulations are used for the synthetic tests, and realistic localization errors are added to the simulated tracks. All three DA methods perform well in cases with the highest spatio-temporal sampling of the flow, and all three methods are relatively robust to the frame rate and magnitude of localization errors. NIPA is more resilient to sparse seeding than FlowFit or VIC#, which exhibit similar performance, but NIPA is also the most expensive technique by some margin. DA reconstructions are superior to interpolation across the board, with a reduction of error up to 80% in the experimental demonstration.
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Che Sidik, Nor Azwadi, Leila Jahanshaloo, Azlin Ismail und Alireza Fazeli. „The Use of Lattice Boltzmann Method for Particulate Flow Analysis“. Applied Mechanics and Materials 695 (November 2014): 413–17. http://dx.doi.org/10.4028/www.scientific.net/amm.695.413.
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In this article, we present a lattice Boltzmann method to treat moving solid particles in a fluid. The scheme uses a uniform Eulerian grid for the flow domain and a Lagrangian grid to trace the dynamics of solid particles. The solid particles in a cavity located on a floor of straight channel were simulated at two difference aspect ratio and wide range of Reynolds numbers. Two different shapes of cavity were selected to investigate their effect of the efficiency of solid particle removal. Current study found that the rate of particle removal is significantly dependence on the Reynolds number of the flow and the shape of the cavity. Excellent agreement with the results computed by other methods indicates the capability of the scheme in predicting particulate problem.
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Hou, Qingzhi, Jiaru Liu, Jijian Lian und Wenhuan Lu. „A Lagrangian Particle Algorithm (SPH) for an Autocatalytic Reaction Model with Multicomponent Reactants“. Processes 7, Nr. 7 (03.07.2019): 421. http://dx.doi.org/10.3390/pr7070421.
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For the numerical simulation of convection-dominated reacting flow problems governed by convection-reaction equations, grids-based Eulerian methods may cause different degrees of either numerical dissipation or unphysical oscillations. In this paper, a Lagrangian particle algorithm based on the smoothed particle hydrodynamics (SPH) method is proposed for convection-reaction equations and is applied to an autocatalytic reaction model with multicomponent reactants. Four typical Eulerian methods are also presented for comparison, including the high-resolution technique with the Superbee flux limiter, which has been considered to be the most appropriate technique for solving convection-reaction equations. Numerical results demonstrated that when comparing with traditional first- and second-order schemes and the high-resolution technique, the present Lagrangian particle algorithm has better numerical accuracy. It can correctly track the moving steep fronts without suffering from numerical diffusion and spurious oscillations.
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Eden, Carsten. „Relating Lagrangian, Residual, and Isopycnal Means“. Journal of Physical Oceanography 42, Nr. 7 (01.07.2012): 1057–64. http://dx.doi.org/10.1175/jpo-d-11-068.1.
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Abstract Three alternative methods of averaging the general conservation equation of a fluid property in a turbulent flow in the Boussinesq approximation are compared: Lagrangian, residual, and isopycnal (or semi-Lagrangian) mean. All methods differentiate consistently but in different ways between effects of advection and irreversible changes of the average property. Because the three average properties differ, the mean transport velocities and the mean irreversible changes in the mean conservation equation differ in general. The Lagrangian and the semi-Lagrangian (or isopycnal) mean frameworks are shown to be approximately equivalent only for weak irreversible changes, small amplitudes of the turbulent fluctuations, and particle excursion predominantly along the mean property gradient. In that case, the divergent Stokes velocity of the Lagrangian mean framework can be replaced in the Lagrangian mean conservation equation by a nondivergent, three-dimensional version of the quasi-Stokes velocity of T. J. McDougall and P. C. McIntosh, for which a closed analytical form for the streamfunction in terms of Eulerian mean quantities is given.
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Fahrenthold, E. P., und J. C. Koo. „Hybrid Particle-Element Bond Graphs for Impact Dynamics Simulation“. Journal of Dynamic Systems, Measurement, and Control 122, Nr. 2 (10.08.1995): 306–13. http://dx.doi.org/10.1115/1.482456.
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Particle methods offer an efficient modeling approach to number of impact dynamics problems not well suited to conventional Eulerian finite difference or Lagrangian finite element methods. Unfortunately, the most popular of these particle methods (smooth particle hydrodynamics) exhibits important deficiencies, in part related to its treatment of boundaries and interparticle tension, and suffers from a rather ad hoc model formulation approach. A hybrid particle-element kinematic scheme and an energy-based, bond graph modeling approach have been combined to produce a new impact dynamics simulation method, free of many problems which have hindered the effective application of various particle and continuum methods. [S0022-0434(00)00602-X]
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Bakry, Mohamed Abdallah, Galal Mahrous Moatimid und Mohamed Mounir Tantawy. „Perihelion advance and stability criterion of a spinning charged test particle in Reissner–Nordström field: Application in earth orbit“. International Journal of Modern Physics A 36, Nr. 10 (10.04.2021): 2150073. http://dx.doi.org/10.1142/s0217751x21500731.
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In this study, a new equation of motion of a spinning charged test particle is examined. This equation is a counterpart of Papapetrou equations in Riemannian geometry when the charge of the particle disappears. By using the Lagrangian approach, the equation of motion of the spinning charged particle is derived. Furthermore, the path deviation of the spinning charged particle is achieved by the same Lagrangian function. The equation of motion of the spinning charged test particle, in the Reissner–Nordström background is entirely solved. The stability criteria of the spinning motion of the charge test particle are discussed. The Perihelion advance and trajectory of a spinning charged test particle, in the Reissner–Nordström space–time, is scrutinized along with two different methods; the first is the perturbation method (Einstein’s method) and the second is described by Kerner et al.[Formula: see text] Moreover, the effect of charge and spin on Perihelion advance are inspected. Additionally, the existing results are matched with the previously cited works. Finally, applications to the Earth’s orbit are also analyzed.
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Spiller, Elaine T., Amarjit Budhiraja, Kayo Ide und Chris K. R. T. Jones. „Modified particle filter methods for assimilating Lagrangian data into a point-vortex model“. Physica D: Nonlinear Phenomena 237, Nr. 10-12 (Juli 2008): 1498–506. http://dx.doi.org/10.1016/j.physd.2008.03.023.
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Tan, Kun. „Simulation of the effect of multi-particle temperature on Al6061 coating porosity based on Coupled Eulerian-Lagrangian (CEL) method“. Mechanics and Advanced Technologies 8, Nr. 3(102) (30.09.2024): 280–88. http://dx.doi.org/10.20535/2521-1943.2024.8.3(102).304079.
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Cold spray is a solid-state deposition technology widely used in additive manufacturing. The particles temperature is mostly used to adjust the porosity of the coating. This article uses Pyhon script to model the multi-particle model; then the multi-particle model is nested in the CEL deposition model to simulate the actual cold spray multi-particle deposition process; The CEL method has the characteristics of high accuracy and robustness and was selected as the simulation method for the multi-particle deposition model. The porosity of the coating is expressed by studying the value of the EVF void area in the Euler domain. Multiple groups of samples were taken on the coating surface to calculate the porosity of each group, and the average value was finally taken as the porosity of the entire coating. Numerical results show that increasing the particle temperature can effectively reduce the porosity of the coating. The average porosity of the coating under the particles temperature conditions are 600 K: 5.08 %; 650 K: 4.02 %; 700 K: 3.58 %; deposition completed the inside of the coating appears to be compacted. The substrate temperature will affect the combination of the coating and the substrate. It is recommended that the temperature difference between the particles and the substrate should not be too large. The CEL method simulates the process of cold spray multi-particle deposition, which is an effective method to observe and predict the porosity of the coating, which is also unachievable by the SPH and ALE methods.
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Wu, Z., W. Birmili, L. Poulain, Z. Wang, M. Merkel, B. Fahlbusch, D. van Pinxteren, H. Herrmann und A. Wiedensohler. „Particle hygroscopicity during atmospheric new particle formation events: implications for the chemical species contributing to particle growth“. Atmospheric Chemistry and Physics 13, Nr. 13 (12.07.2013): 6637–46. http://dx.doi.org/10.5194/acp-13-6637-2013.
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Abstract. This study examines the hygroscopicity of newly formed particles (diameters range 25–45 nm) during two atmospheric new particle formation (NPF) events in the German mid-level mountains during the Hill Cap Cloud Thuringia 2010 (HCCT-2010) field experiment. At the end of the NPF event involving clear particle growth, we measured an unusually high soluble particle fraction of 58.5% at 45 nm particle size. The particle growth rate contributed through sulfuric acid condensation only accounts for around 6.5% of the observed growth rate. Estimations showed that sulfuric acid condensation explained, however, only around 10% of that soluble particle fraction. Therefore, the formation of additional water-soluble matter appears imperative to explain the missing soluble fraction. Although direct evidence is missing, we consider water-soluble organics as candidates for this mechanism. For the case with clear growth process, the particle growth rate was determined by two alternative methods based on tracking the mode diameter of the nucleation mode. The mean particle growth rate obtained from the inter-site data comparison using Lagrangian consideration is 3.8 (± 2.6) nm h−1. During the same period, the growth rate calculated based on one site data is 5.0 nm h−1 using log-normal distribution function method. In light of the fact that considerable uncertainties could be involved in both methods, we consider both estimated growth rates consistent.
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Xue, Pengfei, David Schwab, Xing Zhou, Chenfu Huang, Ryan Kibler und Xinyu Ye. „A Hybrid Lagrangian–Eulerian Particle Model for Ecosystem Simulation“. Journal of Marine Science and Engineering 6, Nr. 4 (26.09.2018): 109. http://dx.doi.org/10.3390/jmse6040109.
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Current numerical methods for simulating biophysical processes in aquatic environments are typically constructed in a grid-based Eulerian framework or as an individual-based model in a particle-based Lagrangian framework. Often, the biogeochemical processes and physical (hydrodynamic) processes occur at different time and space scales, and changes in biological processes do not affect the hydrodynamic conditions. Therefore, it is possible to develop an alternative strategy to grid-based approaches for linking hydrodynamic and biogeochemical models that can significantly improve computational efficiency for this type of linked biophysical model. In this work, we utilize a new technique that links hydrodynamic effects and biological processes through a property-carrying particle model (PCPM) in a Lagrangian/Eulerian framework. The model is tested in idealized cases and its utility is demonstrated in a practical application to Sandusky Bay. Results show the integration of Lagrangian and Eulerian approaches allows for a natural coupling of mass transport (represented by particle movements and random walk) and biological processes in water columns which is described by a nutrient-phytoplankton-zooplankton-detritus (NPZD) biological model. This method is far more efficient than traditional tracer-based Eulerian biophysical models for 3-D simulation, particularly for a large domain and/or ensemble simulations.
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GERASHCHENKO, S., N. S. SHARP, S. NEUSCAMMAN und Z. WARHAFT. „Lagrangian measurements of inertial particle accelerations in a turbulent boundary layer“. Journal of Fluid Mechanics 617 (25.12.2008): 255–81. http://dx.doi.org/10.1017/s0022112008004187.
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Two-dimensional Lagrangian acceleration statistics of inertial particles in a turbulent boundary layer with free-stream turbulence are determined by means of a particle tracking technique using a high-speed camera moving along the side of the wind tunnel at the mean flow speed. The boundary layer is formed above a flat plate placed horizontally in the tunnel, and water droplets are fed into the flow using two different methods: sprays placed downstream from an active grid, and tubes fed into the boundary layer from humidifiers. For the flow conditions studied, the sprays produce Stokes numbers varying from 0.47 to 1.2, and the humidifiers produce Stokes numbers varying from 0.035 to 0.25, where the low and high values refer to the outer boundary layer edge and the near-wall region, respectively. The Froude number is approximately 1.0 for the sprays and 0.25 for the humidifiers, with a small variation within the boundary layer. The free-stream turbulence is varied by operating the grid in the active mode as well as a passive mode (the latter behaves as a conventional grid). The boundary layer momentum-thickness Reynolds numbers are 840 and 725 for the active and passive grid respectively. At the outer edge of the boundary layer, where the shear is weak, the acceleration probability density functions are similar to those previously observed in isotropic turbulence for inertial particles. As the boundary layer plate is approached, the tails of the probability density functions narrow, become negatively skewed, and their peak occurs at negative accelerations (decelerations in the streamwise direction). The mean deceleration and its root mean square (r.m.s.) increase to large values close to the plate. These effects are more pronounced at higher Stokes number. In the vertical direction, there is a slight downward mean deceleration and its r.m.s., which is lower in magnitude than that of the streamwise component, peaks in the buffer region. Although there are free-stream turbulence effects, and the complex boundary layer structure plays an important role, a simple model suggests that the acceleration behaviour is dominated by shear, gravity and inertia. The results are contrasted with inertial particles in isotropic turbulence and with fluid particle acceleration statistics in a boundary layer. The background velocity field is documented by means of hot-wire anemometry and laser Doppler velocimetry measurements. These appear to be the first Lagrangian acceleration measurements of inertial particles in a shear flow.
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Spear, Derek G., Anthony N. Palazotto und Ryan A. Kemnitz. „Modeling and Simulation Techniques Used in High Strain Rate Projectile Impact“. Mathematics 9, Nr. 3 (30.01.2021): 274. http://dx.doi.org/10.3390/math9030274.
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A series of computational models and simulations were conducted for determining the dynamic responses of a solid metal projectile impacting a target under a prescribed high strain rate loading scenario in three-dimensional space. The focus of this study was placed on two different modeling techniques within finite element analysis available in the Abaqus software suite. The first analysis technique relied heavily on more traditional Lagrangian analysis methods utilizing a fixed mesh, while still taking advantage of the finite difference integration present under the explicit analysis approach. A symmetry reduced model using the Lagrangian coordinate system was also developed for comparison in physical and computational performance. The second analysis technique relied on a mixed model that still made use of some Lagrangian modeling, but included smoothed particle hydrodynamics techniques as well, which are mesh free. The inclusion of the smoothed particle hydrodynamics was intended to address some of the known issues in Lagrangian analysis under high displacement and deformation. A comparison of the models was first performed against experimental results as a validation of the models, then the models were compared against each other based on closeness to experimentation and computational performance.
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Ding, Yuanyuan. „An improvement of the Lagrangian analysis method based on particle velocity profiles“. EPJ Web of Conferences 183 (2018): 01023. http://dx.doi.org/10.1051/epjconf/201818301023.
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In general, techniques used in studies on dynamic behaviour of materials could be classified into two categories, namely the split Hopkinson pressure bar technique (SHPB) and the wave propagation technique (WPT). Lagrangian analysis method is one of the most famous methods in WPT. The traditional Lagrangian analysis based on the particle velocity wave-profiles measurements should consider a boundary condition, because it involves integral operations. However, the boundary stress data in some cases cannot be detected or determined by the experimental measures. To tackle this situation, this paper presents a modified Lagrangian analysis method which does not involve the boundary stress computation. Starting from the path-lines method and utilizing the zero-initial condition, the material constitutive stress-strain curves under high strain-rates is deduced from only observing the particle velocity curve measurements. The dynamic stress/strain wave-profiles of the PMMA material, as a paradigm, are numerically studied using the proposed method, which are well in agreement with the theoretical result using the method of characteristics, which confirms the reliability and validity of the presented method.
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Zhou, Kun, und Zhu He. „Monte Carlo simulation of aerosol evolution in a planar mixing layer“. International Journal of Numerical Methods for Heat & Fluid Flow 24, Nr. 8 (28.10.2014): 1769–81. http://dx.doi.org/10.1108/hff-04-2013-0123.
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Purpose – The purpose of this paper is to investigate aerosol evolution in a planar mixing layer from a Lagrangian point of view. After using Monte Carlo (MC) method to simulate the evolution of aerosol dynamics along particles trajectories, the particles size distributions are obtained, which are unavailable in mostly used methods of moments. Design/methodology/approach – Nucleation and growth of dibutyl phthalate (DBP) particles are simulated using the quadrature method of moments in a planar mixing layer, where a fast hot stream with DBP vapor is mixing with a slow cool stream without vapor. Trajectories of aerosol particles are recorded. MC method is used to simulate the aerosol evolution along trajectories. Findings – Investigation on aerosol evolution along the trajectories prompts to classify these trajectories into three groups: first, trajectories away from the active nucleation zone; second, trajectories starting from the active nucleation zone; and third, trajectories crossing over the active nucleation zone. Particle size distributions (psds) along selected representative trajectories are investigated. The psd evolution exhibits interesting behavior due to the synthetic effects of nucleation and condensation. Condensation growth tends to narrow down the psd, and form a sharp front on the side of big particle size. Nucleation is able to broaden the psd through generating the smallest particles. The duration and strength of nucleation have significant effect on the shape of psd. Originality/value – As far as the authors knowledge, it is the first simulation of aerosol evolution that takes a Lagrangian point of view, and uses MC simulation along particles trajectories to provide the particles size distribution.