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Vortex particle-in-cell method for three-dimensional viscous unbounded flow computations

INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN FLUIDS 2000年第1期32卷 29-50页

作者： Liu, CH Doorly, DJ Chung Cheng Inst Technol Dept Aeronaut Engn Rotating Fluids & Vortex Dynam Lab Tao Yuan 335 Taiwan Univ London Imperial Coll Sci Technol & Med Dept Aeronaut London SW7 2BY England

A new vortex particle-in-cell (PIC) method is developed for the computation of three-dimensional unsteady, incompressible viscous flow in an unbounded domain. The method combines the advantages of the Lagrangian particle methods for convection and the use of an Eulerian grid to compute the diffusion and vortex stretching. The velocity boundary conditions used in the method are of Dirichlet-type, and can be calculated using the vorticity field on the grid by the Biot-Savart equation. The present results for the propagation speed of the single vortex ring are in good agreement with the Saffman's model. The applications of the method to the head-on and head-off collisions of the two vortex rings show good agreement with the experimental and numerical literature. Copyright (C) 2000 John Wiley & Sons, Ltd.

关键词： particle-in-cell method viscous unbounded flow Biot-Savart equation

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Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

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Earth and Planetary Physics 2024年第3期8卷 549-563页

作者： Hao Dong ZeBin Cao LiJun Liu YanChong Li SanZhong Li LiMing Dai XinYu Li Frontiers Science Center for Deep Ocean Multispheres and Earth System Key Laboratory of Submarine Geosciences and Prospecting TechniquesMinistry of Education and College of Marine GeosciencesOcean University of ChinaQingdao 266100China State Key Laboratory of Lithospheric Evolution Institute of Geology and GeophysicsChinese Academy of SciencesBeijing 100029China Laboratory for Marine Geology Laoshan LaboratoryQingdao 266237China Department of Earth Science&Environmental Change University of Illinois at Urbana-ChampaignUrbanaIL 61801USA Laboratory of Seismology and Physics of Earth’s Interior School of Earth and Space SciencesUniversity of Science and Technology of ChinaHefei 230026China

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth ***,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising *** phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic *** examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this *** this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data *** have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

关键词： numerical oscillation overshooting and undershooting particle-in-cell method three-dimensional spherical geodynamic modeling energy solver finite element method

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CONTROLLING A VLASOV--POISSON PLASMA BY A particle-in-cell method BASED ON A MONTE CARLO FRAMEWORK

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2024年第4期62卷 1977-2011页

作者： Bartsch, Jan Knopf, Patrik Scheurer, Stefania Weber, Joerg Univ Konstanz Dept Math D-78464 Constance Germany Univ Regensburg Dept Math D-93053 Regensburg Bayern Germany Univ Stuttgart SimTech Cluster D-70569 Stuttgart Germany Univ Vienna Fac Math A-1090 Vienna Austria

The Vlasov--Poisson system describes the time evolution of a plasma in the so-called collisionless regime. The investigation of a high-temperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects of thermonuclear fusion research. In this paper, we formulate and analyze a kinetic optimal control problem for the Vlasov--Poisson system where the control is represented by an external magnetic field. The main goal of such optimal control problems is to confine the plasma to a certain region in phase space. We first investigate the optimal control problem in terms of mathematical analysis, i.e., we show the existence of at least one global minimizer and rigorously derive a first-order necessary optimality condition for local minimizers by the adjoint approach. Then we build a Monte Carlo framework to solve the state equations as well as the adjoint equations by means of a particle-in-cell method, and we apply a nonlinear conjugate gradient method to solve the optimization problem. Eventually, we present numerical experiments that successfully validate our optimization framework.

关键词： Vlasov--Poisson system ensemble optimal control problems multispecies plasma Monte Carlo methods particle-in-cell method magnetic confinement

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A finite-volume particle-in-cell method for the numerical treatment of Maxwell-Lorentz equations on boundary-fitted meshes

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 1999年第4期44卷 461-487页

作者： Munz, CD Schneider, R Sonnendrücker, E Stein, E Voss, U Westermann, T Forschungszentrum Karlsruhe Inst Neutronenphys & Reaktortech Tech & Umwelt D-76021 Karlsruhe Germany Univ Stuttgart Inst Aerodynam & Gasdynam D-70550 Stuttgart Germany Univ Nancy 1 Inst Elie Carton F-54506 Vandoeuvre Nancy France Ecole Polytech Ctr Math Appl F-91128 Palaiseau France FH Karlsruhe Fachbereich Nat Wissensch D-76012 Karlsburg Germany

A new conceptual framework solving numerically the time-dependent Maxwell-Lorentz equations on a non-rectangular quadrilateral mesh in two space dimensions is presented. Beyond a short review of the applied particle treatment based on the particle-in-cell method, a finite-volume scheme for the numerical approximation of the Maxwell equations is introduced using non-rectangular quadrilateral grid arrangements;The coupling of a high-resolution FV Maxwell solver with the PIC method isa new approach in the context of self-consistent charged particle simulation in electromagnetic fields. Furthermore, first simulation results of the time-dependent behaviour of an externally applied-B ion diode developed at the Forschungszentrum in Karlsruhe are presented. Copyright (C) 1999 John Wiley & Sons, Ltd.

关键词： Maxwell-Lorentz equations particle-in-cell method finite-volume schemes

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A Parallel Algorithm for a Semi-Implicit particle-in-cell method with Energy and Charge Conservation

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NUMERICAL ANALYSIS AND APPLICATIONS 2024年第4期17卷 301-312页

作者： Berendeev, E. A. Timofeev, I. V. Novosibirsk State Univ Novosibirsk Russia Russian Acad Sci Budker Inst Nucl Phys Siberian Branch Novosibirsk Russia

The article is devoted to the construction of a parallel algorithm for calculating plasma dynamics by a particle-in-cell method using a semi-implicit scheme that conserves energy and charge. This is a two-stage predictor-corrector scheme. At the prediction stage a semi-implicit Lapenta-type method is used in which an energy-conserving linear current does not satisfy the local Gauss law. At the correction stage the currents, electromagnetic fields, and particle velocities are corrected so that difference laws of energy and charge conservation are satisfied exactly. This approach turns out to be efficient in modeling of multi-scale phenomena with a sufficiently large time step. However, the method is computer time-consuming, since it requires not only solving two systems of linear equations per step, but also reconstructing the entire matrix of the system. The authors have developed a matrix-operator software implementation algorithm for this scheme, which allows efficient paralleling of the calculations and using the various available libraries for work with matrices and solvers for systems of linear equations. To construct the matrix, a row-by-row storage algorithm is used with search for the elements via a hash table, which reduces the memory capacity required, the number of thread synchronizations, and can significantly speed up the calculations. This algorithm has been successfully applied in a computer code, Beren3D.

关键词： parallel algorithm particle-in-cell method solving systems of linear algebraic equations high-performance computing

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Plume expansion of a laser-induced plasma studied with the particle-in-cell method

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APPLIED SURFACE SCIENCE 2002年第1期197卷 229-238页

作者： Ellegaard, O Nedelea, T Schou, J Urbassek, HM Riso Natl Lab Dept Opt & Fluid Dynam DK-4000 Roskilde Denmark Univ Kaiserslautern Dept Phys D-67663 Kaiserslautern Germany Univ So Denmark Doc Dept SDUB DK-5230 Odense Denmark

The initial stage of laser-induced plasma plume expansion from a solid in vacuum and the effect of the Coulomb field have been studied. We have performed a one-dimensional numerical calculation by mapping the charge on a computational grid according to the particle-in-cell (PIC) method of Birdsall et al. It is assumed that the particle ablation from a surface with a fixed temperature takes place as a pulse, i.e. within a finite period of time. A number of characteristic quantities for the plasma plume are compared with similar data for expansion of neutrals as well as fluid models: Density profiles n(x, t), velocity distributions of ions u(x, t), distribution functions for velocities F(nu(x)) of ions or electrons as well as the time dependence of kinetic energy E-kin(t) for both type of particles. We found a significant increase in the velocities of the ions at the expense of field potential energy as well as electron energy. We have estimated the time constant for energy transfer between the electrons and the ions. The scaling of these processes is given by a single parameter determined by the Debye length obtained from the electron density in the plasma outside the surface. (C) 2002 Elsevier Science B.V All rights reserved.

关键词： laser ablation plasma expansion plasma simulation particle-in-cell method

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Plume expansion of a laser-induced plasma studied with the particle-in-cell method

Plume expansion of a laser-induced plasma studied with the p...

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6th International Conferenc on Laser Ablation

关键词： laser ablation plasma expansion plasma simulation particle-in-cell method

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A Deep Learning-Based particle-in-cell method for Plasma Simulations

A Deep Learning-Based Particle-in-Cell Method for Plasma Sim...

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IEEE International Conference on Cluster Computing (Cluster)

作者： Aguilar, Xavier Markidis, Stefano KTH Royal Inst Technol Elect Engn & Comp Sci Sch Stockholm Sweden

ISBN: (纸本)9781728196664

We design and develop a new particle-in-cell (PIC) method for plasma simulations using Deep-Learning (DL) to calculate the electric field from the electron phase space. We train a Multilayer Perceptron (MLP) and a Convolutional Neural Network (CNN) to solve the two-stream instability test. We verify that the DL-based MLP PIC method produces the correct results using the two-stream instability: the DL-based PIC provides the expected growth rate of the two-stream instability. The DL-based PIC does not conserve the total energy and momentum. However, the DL-based PIC method is stable against the cold-beam instability, affecting traditional PIC methods. This work shows that integrating DL technologies into traditional computational methods is a viable approach for developing next-generation PIC algorithms.

关键词： Computational Plasma Physics particle-in-cell method Deep Learning Neural Networks

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Numerical Modeling of Plasma Devices by the particle-in-cell method on Unstructured Grids

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Mathematical Models and Computer Simulations 2018年第2期10卷 198-208页

作者： Dikalyuk, A.S. Kuratov, S.E. All-Russia Research Institute of Automatics (VNIIA) Moscow Russian Federation Institute for Problems of Mechanics (IPMech) Russian Academy of Sciences (RAS) Moscow Russian Federation Moscow Institute of Physics and Technology (MIPT) Moscow Russian Federation

The paper considers methods and algorithms providing the basis for a computer program implementing an axial-symmetric electrostatic version of the particle-in-cell method on unstructured triangular grids. In the presented implementation, the Poisson equation is approximated using the finite volume method. A discrete analog of the Poisson equation is solved by the multigrid method. Charged particle trajectories are calculated using the Boris method. methods for interpolating electrostatic fields on unstructured grids and obtaining the charge density in the computational domain are considered. Special attention is paid to the specifics of implementing these methods in axisymmetric geometry. The developed computer code is tested on the problem of a flat diode operating in the space charge mode. © 2018, Pleiades Publishing, Ltd.

关键词： particle-in-cell method two-dimensional Child–Langmuir problem unstructured triangular grids

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Numerical thermalization of two-dimensional plasmas in the presence of binary collisions with the particle-in-cell method 41

Numerical thermalization of two-dimensional plasmas in the p...

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41st IEEE International Conference on Plasma Science, ICOPS 2014 and the 20th IEEE International Conference on High-Power particle Beams, BEAMS 2014

作者： Koh, W.S. Ding, W.J. Lai, P.-Y. Chen, S.H. Lin-Liu, Y.R. ASTAR Institute of High Performance Computing Singapore138632 Singapore Department of Physics National Central University Jung-Li32001 Taiwan

ISBN: (纸本)9781479927111

Summary form only given. Numerical self-heating and thermalization are two unphysical artifacts in particle-in-cell (PIC) simulations due to the implicit assumptions used in the numerical method. Numerical self-heating in plasma simulations can typically be suppressed by using higher order finite-difference methods, field smoothing and particle weighting schemes. On the other hand, numerical thermalization is associated with the granularity of the particles that introduces relaxation in the velocity distribution functions (i.e. the particle velocity distribution approaches Maxwellian). In 2D collisionless plasma simulations, the rate of relaxation has been shown to be proportional to 1/ND, where ND is the number of particles per Debye length1. This scaling has been illustrated to be true in several previous works using electrostatic PIC codes. Here we will focus on the study of numerical thermalization for 2D collisional plasma using an in-house electromagnetic PIC (IPIC or Ihpc particle-In-cell) code. The binary collision model in IPIC is implemented based on the Fokker-Planck Collision operator to mimic Coulomb collisions in real plasmas2. Our numerical results confirm that without collisions, the 1/ND scaling remains intact as expected. However, in the presence of binary collisions, the relaxation rate is also scaled with 1/ND at small ND, but the scaling parameter varies distinctly as ND increases. The implications of this previously unidentified observation will be discussed.

关键词： finite difference methods plasma collision processes plasma simulation plasma thermodynamics 1/ND scaling 2D collisional plasma 2D collisionless plasma simulations Coulomb collisions Debye length Fokker-Planck Collision operator IPIC code Ihpc particle-In-cell binary collision model electrostatic PIC codes field smoothing higher order finite-difference methods in-house electromagnetic PIC numerical method numerical self-heating numerical thermalization particle granularity particle velocity distribution particle weighting schemes particle-in-cell method particle-in-cell simulations real plasmas relaxation rate scaling parameter two-dimensional plasmas unphysical artifacts velocity distribution function Computational modeling Educational institutions High performance computing Numerical models Physics Plasma simulation

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