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Academic literature on the topic 'Lagrangian particle methods'

Author: Grafiati

Published: 25 January 2025

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Journal articles on the topic "Lagrangian particle methods"

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Chakraborty, Rishiraj, Aaron Coutino, and Marek Stastna. "Particle clustering and subclustering as a proxy for mixing in geophysical flows." Nonlinear Processes in Geophysics 26, no. 3 (September 16, 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, and S. P. Xiao. "Stable particle methods based on Lagrangian kernels." Computer Methods in Applied Mechanics and Engineering 193, no. 12-14 (March 2004): 1035–63. http://dx.doi.org/10.1016/j.cma.2003.12.005.

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Healy, D. P., and 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, no. 2059 (June 15, 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, and Jinghua Wang. "Quadric SFDI for Laplacian Discretisation in Lagrangian Meshless Methods." Journal of Marine Science and Application 19, no. 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, and 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, and Frédérique Charles. "From particle methods to forward-backward Lagrangian schemes." SMAI journal of computational mathematics 4 (March 27, 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, and Andy M. Booth. "A comparison of Eulerian and Lagrangian methods for vertical particle transport in the water column." Geoscientific Model Development 16, no. 18 (September 19, 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, and 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, no. 10 (September 26, 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., and H. Rasmussen. "Numerical Methods for Viscous Flows With Moving Boundaries." Applied Mechanics Reviews 42, no. 12 (December 1, 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, and 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, no. 2199 (March 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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Dissertations / Theses on the topic "Lagrangian particle methods"

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Fleissner, Florian. "Parallel object oriented simulation with Lagrangian particle methods." Aachen Shaker, 2009. http://d-nb.info/1000976742/04.

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Fleissner, Florian [Verfasser]. "Parallel Object Oriented Simulation with Lagrangian Particle Methods / Florian Fleissner." Aachen : Shaker, 2010. http://d-nb.info/1124364129/34.

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Hosein, Falahaty. "Enhanced fully-Lagrangian particle methods for non-linear interaction between incompressible fluid and structure." Kyoto University, 2018. http://hdl.handle.net/2433/235070.

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Grabel, Michael Z. "A Lagrangian/Eulerian Approach for Capturing Topological Changes in Moving Interface Problems." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563527241172213.

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Rieth, Martin [Verfasser], and Andreas [Akademischer Betreuer] Kempf. "Large eddy and direct numerical simulation of single and multiphase flows relying on lagrangian particle methods / Martin Rieth ; Betreuer: Andreas Kempf." Duisburg, 2018. http://d-nb.info/1153337916/34.

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Pinto, Wesley José Nunes. "Aplicação do método lagrangiano SPH (Smoothed Particle Hydrodynamics ) para a solução do problema das cavidades." Universidade Federal do Espírito Santo, 2013. http://repositorio.ufes.br/handle/10/6144.

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Made available in DSpace on 2016-12-23T14:04:30Z (GMT). No. of bitstreams: 1 Wesley Jose Nunes Pinto.pdf: 2090367 bytes, checksum: e676fde8423a3a2cfeac61da24020ea8 (MD5) Previous issue date: 2013-08-19
Neste estudo foi aplicado do método numérico, sem malhas, baseado em partículas, denominado SPH (Smoothed Particles Hydrodynamics). E um código numérico na linguagem computacional FORTRAN foi utilizado para solucionar as equações de Navier-Stokes. O clássico problema da literatura da dinâmica dos fluidos Computacional, denotado como problema da cavidade quadrada bidimensional (Shear-Driven Cavity Flow) , foi estudado com a intenção de verificar o comportamento do código numérico em relação a resultados específicos já existentes do assunto. O citado problema físico das cavidades abertas é amplamente empregado como benchmark, visando a validação do método numérico utilizado no trabalho desenvolvido na pesquisa. O trabalho de análise e validação do código numérico foi dividido em três seções: a primeira lista as localizações dos centros dos vórtices principais gerados pelo escoamento na aresta superior das cavidades; a segunda plota os perfis das componentes das velocidades centrais das cavidades; e a terceira: lista os desvios absolutos dos perfis das velocidades centrais do presente trabalho, comparados com dados de outros estudos. Constata-se que o método SPH apresentou boa acurácia nas simulações realizadas, obtendo boa concordância entre os resultados das simulações dinâmicas com os dados de referências, validando-se o modelo numérico proposto, tendo melhores resultados para baixos números de Reynolds
In this study, it was applied the numerical method, grid-free, based on particles named SPH (Smoothed Particles Hydrodynamics). Also, a numerical code in the computer language FORTRAN was used to solve the Navier-Stokes Equations. This classic problem of the literature related to Computational Fluid Dynamics indicated as Shear-Driven Cavity Flow was studied to check the behavior of the numerical code regarding specific existing results. Such problem is highly used as Benchmark, aiming the validation of the numerical method used to develop the research. The analysis and validation of the numerical code was divided into three sections: the first one lists the location of the centre of the main vortex generated by the flow of the upper edge of the cavities; the second one plots the profiles of the components of the central speed of the cavities; the third one lists the absolute deviation of the profiles of the central speed of this study compared with other cases data. It is established that the SPH Method presented accuracy in the performed simulations, in a consonance between the results of the dynamic simulations and the reference data, thus the proposed numerical model was validated with better results for low Reynolds numbers

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Góes, Marciana Lima. "Desenvolvimento de um simulador numérico empregando o método Smoothed Particle Hydrodynamics para a resolução de escoamentos incompressíveis. Implementação computacional em paralelo (CUDA)." Universidade do Estado do Rio de Janeiro, 2012. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=4029.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Neste trabalho, foi desenvolvido um simulador numérico baseado no método livre de malhas Smoothed Particle Hydrodynamics (SPH) para a resolução de escoamentos de fluidos newtonianos incompressíveis. Diferentemente da maioria das versões existentes deste método, o código numérico faz uso de uma técnica iterativa na determinação do campo de pressões. Este procedimento emprega a forma diferencial de uma equação de estado para um fluido compressível e a equação da continuidade a fim de que a correção da pressão seja determinada. Uma versão paralelizada do simulador numérico foi implementada usando a linguagem de programação C/C++ e a Compute Unified Device Architecture (CUDA) da NVIDIA Corporation. Foram simulados três problemas, o problema unidimensional do escoamento de Couette e os problemas bidimensionais do escoamento no interior de uma Cavidade (Shear Driven Cavity Problem) e da Quebra de Barragem (Dambreak).
In this work a numerical simulator was developed based on the mesh-free Smoothed Particle Hydrodynamics (SPH) method to solve incompressible newtonian fluid flows. Unlike most existing versions of this method, the numerical code uses an iterative technique in the pressure field determination. This approach employs a differential state equation for a compressible fluid and the continuity equation to calculate the pressure correction. A parallel version of the numerical code was implemented using the Programming Language C/C++ and Compute Unified Device Architecture (CUDA) from the NVIDIA Corporation. The numerical results were validated and the speed-up evaluated for an one-dimensional Couette flow and two-dimensional Shear Driven Cavity and Dambreak problems.

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Freitas, Mayksoel Medeiros de. "Simulação de escoamentos incompressíveis empregando o método Smoothed Particle Hydrodynamics utilizando algoritmos iterativos na determinação do campo de pressões." Universidade do Estado do Rio de Janeiro, 2013. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=4839.

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Nesse trabalho, foi desenvolvido um simulador numérico (C/C++) para a resolução de escoamentos de fluidos newtonianos incompressíveis, baseado no método de partículas Lagrangiano, livre de malhas, Smoothed Particle Hydrodynamics (SPH). Tradicionalmente, duas estratégias são utilizadas na determinação do campo de pressões de forma a garantir-se a condição de incompressibilidade do fluido. A primeira delas é a formulação chamada Weak Compressible Smoothed Particle Hydrodynamics (WCSPH), onde uma equação de estado para um fluido quase-incompressível é utilizada na determinação do campo de pressões. A segunda, emprega o Método da Projeção e o campo de pressões é obtido mediante a resolução de uma equação de Poisson. No estudo aqui desenvolvido, propõe-se três métodos iterativos, baseados noMétodo da Projeção, para o cálculo do campo de pressões, Incompressible Smoothed Particle Hydrodynamics (ISPH). A fim de validar os métodos iterativos e o código computacional, foram simulados dois problemas unidimensionais: os escoamentos de Couette entre duas placas planas paralelas infinitas e de Poiseuille em um duto infinito e foram usadas condições de contorno do tipo periódicas e partículas fantasmas. Um problema bidimensional, o escoamento no interior de uma cavidade com a parede superior posta em movimento, também foi considerado. Na resolução deste problema foi utilizado o reposicionamento periódico de partículas e partículas fantasmas.
In this work, we have developed a numerical simulator (C/C++) to solve incompressible Newtonian fluid flows, based on the meshfree Lagrangian Smoothed Particle Hydrodynamics (SPH) Method. Traditionally, two methods have been used to determine the pressure field to ensure the incompressibility of the fluid flow. The first is calledWeak Compressible Smoothed Particle Hydrodynamics (WCSPH) Method, in which an equation of state for a quasi-incompressible fluid is used to determine the pressure field. The second employs the Projection Method and the pressure field is obtained by solving a Poissons equation. In the study developed here, we have proposed three iterative methods based on the Projection Method to calculate the pressure field, Incompressible Smoothed Particle Hydrodynamics (ISPH) Method. In order to validate the iterative methods and the computational code we have simulated two one-dimensional problems: the Couette flow between two infinite parallel flat plates and the Poiseuille flow in a infinite duct, and periodic boundary conditions and ghost particles have been used. A two-dimensional problem, the lid-driven cavity flow, has also been considered. In solving this problem we have used a periodic repositioning technique and ghost particles.

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Cocle, Roger. "Combining the vortex-in-cell and parallel fast multipole methods for efficient domain decomposition simulations : DNS and LES approaches." Université catholique de Louvain, 2007. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-08172007-165806/.

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This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.

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Vidal, Seguí Yolanda. "Mesh-Free Methods for Dynamic Problems. Incompressibility and Large Strain." Doctoral thesis, Universitat Politècnica de Catalunya, 2005. http://hdl.handle.net/10803/6709.

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This thesis makes two noteworthy contributions in the are of mesh-free methods: a Pseudo-Divergence-Free (PDF) Element Free Galerkin (EFG) method which alleviates the volumetric locking and a Stabilized Updated Lagrangian formulation which allows to solve fast-transient dynamic problems involving large distortions. The thesis is organized in the following way.
First of all, this thesis dedicates one chapter to the state of the art of mesh-free methods. The main reason is because there are many mesh-free methods that can be found in the literature which can be based on different ideas and with different properties. There is a real need of classifying, ordering and comparing these methods: in fact, the same or almost the same method can be found with different names in the literature.
Secondly, a novel improved formulation of the (EFG) method is proposed in order to alleviate volumetric locking. It is based on a pseudo-divergence-free interpolation. Using the concept of diffuse derivatives an a convergence theorem of these derivatives to the ones of the exact solution, the new approximation proposed is obtained imposing a zero diffuse divergence. In this way is guaranteed that the method verifies asymptotically the incompressibility condition and in addition the imposition can be done a priori. This means that the main difference between standard EFG and the improved method is how is chosen the interpolation basis. Modal analysis and numerical results for two classical benchmark tests in solids corroborate that, as expected, diffuse derivatives converge to the derivatives of the exact solution when the discretization is refined (for a fixed dilation parameter) and, of course, that diffuse divergence converges to the exact divergence with the expected theoretical rate. For standard EFG the typical convergence rate is degrade as the incompressible limit is approached but with the improved method good results are obtained even for a nearly incompressible case and a moderately fine discretization. The improved method has also been used to solve the Stokes equations. In this case the LBB condition is not explicitly satisfied because the pseudo-divergence-free approximation is employed. Reasonable results are obtained in spite of the equal order interpolation for velocity and pressure.
Finally, several techniques have been developed in the past to solve the well known tensile instability in the SPH (Smooth Particle Hydrodynamics) mesh-free method. It has been proved that a Lagrangian formulation removes completely the instability (but zero energy modes exist). In fact, Lagrangian SPH works even better than the Finite Element Method in problems involving distortions. Nevertheless, in problems with very large distortions a Lagrangian formulation will need of frequent updates of the reference configuration. When such updates are incorporated then zero energy modes are more likely to be activated. When few updates are carried out the error is small but when updates are performed frequently the solution is completely spoilt because of the zero energy modes. In this thesis an updated Lagrangian formulation is developed. It allows to carry out updates of the reference configuration without suffering the appearance of spurious modes. To update the Lagrangian formulation an incremental approach is used: an intermediate configuration will be the new reference configuration for the next time steps. It has been observed that this updated formulation suffers from similar numerical fracture to the Eulerian case. A modal analysis has proven that there exist zero energy modes. In the paper the updated Lagrangian method is exposed in detail, a stability analysis is performed and finally a stabilization technique is incorporated to preclude spurious modes.

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Books on the topic "Lagrangian particle methods"

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Next Free-Lagrange Conference (1990 Moran, Wyo.). Advances in the Free-Lagrange method: Including contributions on adaptive gridding and the smooth particle hydrodynamics method : proceedings of the Next Free-Lagrange Conference held at Jackson Lake Lodge, Moran, Wyoming, USA, 3-7 June 1990. Berlin: Springer-Verlag, 1991.

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United States. National Aeronautics and Space Administration., ed. Oblique hypervelocity impact simulation for multi-layer orbital debris shielding (NAG 9-744): Final report. [Washington, DC: National Aeronautics and Space Administration, 1996.

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United States. National Aeronautics and Space Administration., ed. Oblique hypervelocity impact simulation for multi-layer orbital debris shielding (NAG 9-744): Final report. [Washington, DC: National Aeronautics and Space Administration, 1996.

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Trease, Harold E., Martin F. Fritts, and W. Patrick Crowley. Advances in the Free-Lagrange Method: Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method. Springer, 2014.

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Fritts, M. J., H. E. Trease, and Free-Lagrange Conference (1990 Moran Wyo ). Next. Advances in the Free-Lagrange Method: Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method : Proceedings of the (Lecture Notes in Physics). Springer, 1992.

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Kachelriess, Michael. Classical mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802877.003.0001.

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This chapter reviews those concepts of classical mechanics which are essential for progressing towards quantum theory. The Lagrangian and Hamiltonian formulation of classical mechanics are derived from action principles. The Green function method is illustrated and the action of a relativistic point particle recalled.

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Rajeev, S. G. Finite Difference Methods. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0014.

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This chapter offers a peek at the vast literature on numerical methods for partial differential equations. The focus is on finite difference methods (FDM): approximating differential operators by functions of difference operators. Padé approximants (Fornberg) give a unifying principle for deriving the various stencils used by numericists. Boundary value problems for the Poisson equation and initial value problems for the diffusion equation are solved using FDM. Numerical instability of explicit schemes are explained physically and implicit schemes introduced. A discrete version of theClebsch formulation of incompressible Euler equations is proposed. The chapter concludes with the radial basis function method and its application to a discrete version of the Lagrangian formulation of Navier–Stokes.

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Mann, Peter. Coordinates & Constraints. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0006.

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This short chapter introduces constraints, generalised coordinates and the various spaces of Lagrangian mechanics. Analytical mechanics concerns itself with scalar quantities of a dynamic system, namely the potential and kinetic energies of the particle; this approach is in opposition to Newton’s method of vectorial mechanics, which relies upon defining the position of the particle in three-dimensional space, and the forces acting upon it. The chapter serves as an informal, non-mathematical introduction to differential geometry concepts that describe the configuration space and velocity phase space as a manifold and a tangent, respectively. The distinction between holonomic and non-holonomic constraints is discussed, as are isoperimetric constraints, configuration manifolds, generalised velocity and tangent bundles. The chapter also introduces constraint submanifolds, in an intuitive, graphic format.

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Mann, Peter. Partial Differentiation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0032.

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This short chapter discusses the Legendre transform, which is used in mechanics to convert between the Lagrangian and the Hamiltonian formulations. The Legendre transform is a mathematical tool that can be used to convert the variables of a function through the methods of partial differentiation in a one-to-one fashion. Developed by Adrien-Marie Legendre in the nineteenth century, it is also central to converting between action principles, generating functions and thermodynamic potentials. By using the Legendre transform, two variables can be expressed in four different ways, via the idea of conjugate pairs; it just depends on what differential quantity is subtracted. Variables that are not considered in the transformation are called passive variables, whiles the important ones are the active variables. The information in this chapter provides the background for many of the other chapters in this book.

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Book chapters on the topic "Lagrangian particle methods"

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Cottet, Georges-Henri, and Petros Koumoutsakos. "High Order Semi-Lagrangian Particle Methods." In Lecture Notes in Computational Science and Engineering, 103–17. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65870-4_6.

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Cottet, Georges-Henri. "Semi-Lagrangian Particle Methods for Hyperbolic Equations." In Theory, Numerics and Applications of Hyperbolic Problems I, 395–411. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91545-6_31.

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Zannetti, Paolo, and Nazik Al-Madani. "Simulation of Transformation, Buoyancy and Removal Processes by Lagrangian Particle Methods." In Air Pollution Modeling and Its Application IV, 733–44. Boston, MA: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4613-2455-3_39.

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Grašič, Boštjan, Marija Zlata Božnar, and Primož Mlakar. "New Methods for Improvement of the Computational Efficiency of the Lagrangian Particle Dispersion Model." In Air Pollution Modeling and its Application XXI, 69–73. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-1359-8_12.

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Xiao, Chang, Wei Liu, Jianying Wu, and Dingyuan Zhang. "Seismic Response Analysis of Full Containment LNG Storage Tank Using Coupled Eulerian–Lagrangian and Smoothed Particle Hydrodynamics Methods." In Computational and Experimental Simulations in Engineering, 1251–62. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-42515-8_87.

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Mahomed, F. M., A. H. Kara, and P. G. L. Leach. "Symmetries of Particle Lagrangians." In Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, 273–76. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2050-0_28.

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Wittig, Hartmut. "QCD on the Lattice." In Particle Physics Reference Library, 137–262. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38207-0_5.

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AbstractSince Wilson’s seminal papers of the mid-1970s, the lattice approach to Quantum Chromodynamics has become increasingly important for the study of the strong interaction at low energies, and has now turned into a mature and established technique. In spite of the fact that the lattice formulation of Quantum Field Theory has been applied to virtually all fundamental interactions, it is appropriate to discuss this topic in a chapter devoted to QCD, since by far the largest part of activity is focused on the strong interaction. Lattice QCD is, in fact, the only known method which allows ab initio investigations of hadronic properties, starting from the QCD Lagrangian formulated in terms of quarks and gluons.

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Gittings, Michael L. "TRIX: A free-lagrangian hydrocode." In Advances in the Free-Lagrange Method Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method, 28–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54960-9_36.

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Dukowicz, John K., and Bertrand J. A. Meltz. "Vorticity errors in multidimensional Lagrangian codes." In Advances in the Free-Lagrange Method Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method, 289–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54960-9_62.

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Rotach, Mathias W., and Stefan Schwere. "A Method to Speed up a Lagrangian Stochastic Particle Dispersion Model." In Air Pollution Modeling and Its Application XIII, 509–17. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4153-0_52.

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Conference papers on the topic "Lagrangian particle methods"

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Singh, Puneet, and Peretz Friedmann. "A Computational Fluid Dynamics Based Viscous Vortex Particle Method for Coaxial Rotor Interaction Calculations." In Vertical Flight Society 73rd Annual Forum & Technology Display, 1–8. The Vertical Flight Society, 2017. http://dx.doi.org/10.4050/f-0073-2017-12002.

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The coaxial rotor in hover and forward flight experiences complex unsteady aerodynamic interaction effects. Standard methods used for isolated rotor analysis are not adequate for obtaining the unsteady loads and wake. More accurate and computationally efficient approaches are required. The viscous vortex particle approach based on the Lagrangian formulation of the incompressible Navier-Stokes equations is a grid free method suitable for capturing the vortex wake interaction over long distances. The rational function approximation of unsteady airfoil loads from a CFD database is used to reduce computational effort and improve accuracy of load calculations. The vortex particle method and the rational function approximation are combined and applied to evaluate performance, wake evolution and loads for a coaxial rotor system in hover. The isolated and coaxial rotor thrust and torque performance were accurately predicted. The unsteady hub loads in hover were calculated using this technique. The blade passage frequency was a dominant source of oscillations in aerodynamic loading. The effect of the rotor wake system was determined and a comparison of the aerodynamic loading models was conducted.

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Billac, Thomas, Rodney Thomson, Mark Battley, and Raj Das. "Water Impact of Helicopter Subfloor Panels." In Vertical Flight Society 71st Annual Forum & Technology Display, 1–13. The Vertical Flight Society, 2015. http://dx.doi.org/10.4050/f-0071-2015-10148.

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The hydroelastic structural response excited during helicopter ditching involves extremely complex physics to capture through analytical solutions. The Smoothed Particle Hydrodynamics (SPH) method has proven its suitability to represent free-surface flows, and when coupled with traditional Lagrangian Finite Element (FE) method enables water impact problems to be simulated with reasonable computational times. The water impact of thin aluminum and carbon fiber composite panels was chosen as a benchmark case to determine the accuracy of meshless methods to predict loads during water entry. Experiments were conducted using a servo-hydraulic water impact system with various impact conditions to support the validation of numerical models. High sensitivity was observed to the selected fluid equation of state and to the smoothing length factor. The FE/SPH models accurately predicted the loads experienced by the panels during water entry. Deformations of the panels were also consistent with experimental measurements although the accuracy of the predictions may be improved with a refined representation of the specimen restraints.

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Stock, Mark J., and Adrin Gharakhani. "Solution-Responsive Particle Size Adaptivity in Lagrangian Vortex Particle Methods." In ASME 2021 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/fedsm2021-65621.

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Abstract In order to minimize the computational resources necessary for a given level of accuracy in a Lagrangian Vortex Particle Method, a novel particle core size adaptivity scheme has been created. The method adapts locally to the solution while preventing large particle size gradients, and optionally adapts globally to focus effort on important regions. It is implemented in the diffusion solver, which uses the Vorticity Redistribution Method, by allowing and accounting for variations in the core radius of participating particles. We demonstrate the effectiveness of this new method on the diffusion of a δ-function and impulsively started flow over a circular cylinder at Re = 9,500. In each case, the adaptive method provides solutions with marginal loss of accuracy but with substantially fewer computational elements.

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Dembele, Jean Marie, and Christophe Cambier. "Improving Lagrangian methods: toward an agent-particle based method." In 2nd International ICST Conference on Simulation Tools and Techniques. ICST, 2009. http://dx.doi.org/10.4108/icst.simutools2009.5658.

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O’Donnell, Jacob, Michael Smith, and Paul Cavallaro. "Comparison of Residual Stresses in Cold Spray Coatings: Lagrangian vs. Eulerian Finite Element Methods." In ASME 2022 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/imece2022-93902.

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Abstract Cold spray is a novel thermal spray process in which a gas at high temperature and pressure deposits solid particles onto a substrate material. Current research utilizes a variety of methods of modeling techniques in order to capture the physics and dynamics of a cold spray particle impact, incorporating elements of the Lagrangian and Eulerian modeling methods. This research modeled the cold spray event of single and multi-particle impacts using Lagrangian and Eulerian methods. The material of both the particle and substrate are a standard Aluminum 6061-T6 alloy. The objectives of the models are to: (1) obtain particle and substrate deformations and residual stresses as functions of particle velocity, particle temperature, and substrate temperature; (2) establish the minimum number of successive particle layers such that the substrate residual stresses reach steady state; and (3) identify numerical limitations in the Lagrangian and Eulerian modeling methods using ABAQUS/Explicit. The Lagrangian method predicted a maximum von Mises stress 23.72% lower than that of the Eulerian. The Lagrangian models allowed for discrete node tracking, however, thus allowing for improved surface definitions and transient material point tracking. The Eulerian models also better handled the plastic deformation and resultant temperature generation within the model, and thus were able to handle multiple particle impacts while the Lagrangian could not. The multi-particle models using the Eulerian method reported that seven particles were required for the substrate steady-state stress to remain independent of subsequent particle impacts. Concentric initial position multi-particle models saw a maximum 42.00% reduction in von Mises stress compared to the single-particle models and a maximum 53.18% reduction compared to multi-particle modes with randomized initial particle positions. Multi-particle impacts demonstrated a reduction in stress when compared to the single particle impact due to the increased thermal softening present.

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Le Lostec, Nechtan, Philippe Villedieu, and Olivier Simonin. "Comparison Between Grad’s and Quadrature-Based Methods of Moments for the Numerical Simulation of Unsteady Particle-Laden Flows." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78360.

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We present here a new method of moments for the numerical simulation of particle-laden flows. The closure needed in Eulerian methods relies on writing the kinetic descriptor, the velocity destribution function, as a sum of delta-functions instead of the one-delta-function or close-to-Maxwellian assumption in existing methods. The closure velocity distribution function parameters are computed from the transported moments using a quadrature method. Simulation results are compared to those of a close-to-Maxwellian-based Eulerian method and those of a reference Lagrangian simulation, considering only transport and drag of particles in a Taylor-Green fluid flow. For a particular Stokes number of 1 the velocity distribution function is far from equilibrium and particle trajectory crossing is an important feature. We find that the quadrature-based method performs better than the close-to-equilibrium-based method, giving moment profiles closer to those of the Lagrangian reference simulation. However significant differences still remain between quadrature-based and Lagrangian methods results.

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Huilier, Daniel. "Lagrangian Simulation of Gas-Solid Flows in Homogeneous Isotropic Turbulence." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2049.

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Abstract A Lagrangian approach is developed to describe particle’s dispersion in a stationary, homogeneous and isotropic turbulent flow. Obviously, the particles’ dispersion is influenced by the fluid velocity fluctuations, which are classically simulated by a Monte Carlo process or Markov chains. However, some studies have shown the restrictions of these methods generating the fluid turbulent velocity and have suggested improvements to ensure that the Lagrangian model accounts for the three main effects governing the dispersion in gas-particle flows, namely the inertia, crossing trajectories and continuity effects. The first aim of this paper is to present an improved Lagrangian model which integrates the spatio-temporal characteristics of the fluid turbulence experienced by the particle. The agreement between the numerical results obtained and the analytical expressions derived by Wang and Stock (1993) will be very satisfying. Another interest is to investigate the role of the traditionally-neglected and troublesome added mass and history terms in numerical studies when long time dispersion of inertial particles is the primary concern. Indeed, we will observe that for a large range of values of the ratio of particle to fluid density, these non-stationary forces have statistically no influence on the characteristics of the turbulent particle dispersion and can be safely omitted.

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Xu, Yiban, Michael A. Krammen, Guoqiang Wang, Jesse S. Fisher, and Zeses Karoutas. "Analysis of Particle Transfer Behavior in Fuel Rod Bundles Using CFD Lagrangian Particle Tracking Method." In 2021 28th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/icone28-66793.

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Abstract Crud has been observed on the fuel rod surfaces in a variety of fuel designs around the world, and in some limited situations fuel performance was compromised due to crud-induced power shift (CIPS) and/or crud-induced localized corrosion (CILC). It is generally believed that crud deposition depends on fuel rod surface sub-cooled nucleate boiling, coolant chemistry and the availability of particles from component corrosion or from reinserted fuel. The formation, release, and accumulation of crud on the fuel and its influence on CIPS and/or CILC is a complicated process involving multi-physics phenomena. This study uses Computational Fluid Dynamics (CFD) Lagrangian Particle Tracking (LPT) techniques in analysis of particle transfer behavior in fuel rod bundles focusing on flow swirl and turbulence impacts. It is hoped that high fidelity CFD results can provide insights into particle transfer behaviors in the bulk coolant as well as near the fuel rods, which may provide guidance for model development of lumped or integrated analysis methods. The CFD model was built based on the best practices learned from previous single-phase analyses. The LPT options, including particle injectors, forces on particles, and solver settings, were verified by comparing the simulated results to the test data from simple geometry with various particle sizes, covering deposition mechanisms in diffusion-, turbulent- and inertial-dominated regimes. The tested model then was applied to Westinghouse fuel designs with and without Intermediate Flow Mixing (IFM) grids. Particle concentration and size distributions in the coolant around fuel rods were obtained and the effects of grid induced swirl flow on particle transfer were identified. The analysis results may be included in lumped or integrated crud formation/release analysis methods. Limitations and potential improvements of this analysis method are also discussed.

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Furuhata, T., Sh Tanno, and Takatoshi Miura. "COMPARATIVE STUDY OF TWO-PHASE (PARTICLE LADEN) JET CALCULATION METHODS (LAGRANGIAN AND EULERIAN METHODS)." In ICLASS 94. Connecticut: Begellhouse, 2023. http://dx.doi.org/10.1615/iclass-94.660.

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Culp, David B., and Xia Ma. "Modeling Fragmentation within Pagosa Using Particle Methods." In 2019 15th Hypervelocity Impact Symposium. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/hvis2019-085.

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Abstract The mechanics involved in shock physics often involves materials undergoing large deformations being subjected to high strain rates and temperature variations. When considering high-velocity impacts and explosions, metals experience plastic flow, dynamic failures and fragmentation that are often too complex for a Lagrangian method, such as the finite element method, to properly resolve. Conversely, Eulerian methods are simple to setup, but often result in numerical diffusion errors [1]. These unpleasantries can be skirted by using an alternative technique that incorporates a blend of these aforementioned methods. FLIP+MPM (FLuid Implicit Particle + Material Point Method) employs Lagrangian points to track state quantities associated with materials as strength, as well as conserved quantities, such as mass. Concurrently, an Eulerian grid is used to calculate gradient fields and incorporate an algorithm that carries out the hydrodynamics [2]. By incorporating the FLIP+MPM method into Los Alamos National Laboratory’s Pagosa hydrodynamics code, massively parallel architectures may be employed to solve such problems as those including fragmentation, plastic flow and fluid-structure interaction. This paper will begin with a mathematical description of the FLIP+MPM technique and describe how it fits into Pagosa. After a description of the implementation, the capabilities of this numerical technique are highlighted by simulating fragmentation as a result of high velocity impacts and explosions. Several strength and damage models will be exercised to demonstrate the code’s flexibility. Comparison of the different models’ fragment size distributions are given and discussed.

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Reports on the topic "Lagrangian particle methods"

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Trahan, Corey, Jing-Ru Cheng, and Amanda Hines. ERDC-PT : a multidimensional particle tracking model. Engineer Research and Development Center (U.S.), January 2023. http://dx.doi.org/10.21079/11681/48057.

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This report describes the technical engine details of the particle- and species-tracking software ERDC-PT. The development of ERDC-PT leveraged a legacy ERDC tracking model, “PT123,” developed by a civil works basic research project titled “Efficient Resolution of Complex Transport Phenomena Using Eulerian-Lagrangian Techniques” and in part by the System-Wide Water Resources Program. Given hydrodynamic velocities, ERDC-PT can track thousands of massless particles on 2D and 3D unstructured or converted structured meshes through distributed processing. At the time of this report, ERDC-PT supports triangular elements in 2D and tetrahedral elements in 3D. First-, second-, and fourth-order Runge-Kutta time integration methods are included in ERDC-PT to solve the ordinary differential equations describing the motion of particles. An element-by-element tracking algorithm is used for efficient particle tracking over the mesh. ERDC-PT tracks particles along the closed and free surface boundaries by velocity projection and stops tracking when a particle encounters the open boundary. In addition to passive particles, ERDC-PT can transport behavioral species, such as oyster larvae. This report is the first report of the series describing the technical details of the tracking engine. It details the governing equation and numerical approaching associated with ERDC-PT Version 1.0 contents.

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Enright, Douglas, Frank Losasso, and Ronald Fedkiw. A Fast and Accurate Semi-Lagrangian Particle Level Set Method. Fort Belvoir, VA: Defense Technical Information Center, April 2004. http://dx.doi.org/10.21236/ada479118.

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