An efficient scheme for convection-dominated transport

Hitchon, W. N. G.; Koch, Daniel; Adams, James B.

doi:10.1016/0021-9991(89)90223-4

Cited by 65 publications

(33 citation statements)

References 12 publications

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“…Consequently, and again in principle, the only consideration entering into a choice between the particle-in-cell method and other competing algorithms is numerical efficiency. The main alternatives to the particle-in-cell method are various finite difference methods, such as the well-known "convective scheme" [11,12]. Both the convective scheme and the particle-in-cell method require that finite intervals in space and time be specified as part of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

Kinetic properties of particle-in-cell simulations compromised by Monte Carlo collisions

Turner

2006

Physics of Plasmas

103

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The particle-in-cell method with Monte Carlo collisions is frequently employed when a detailed kinetic simulation of a weakly collisional plasma is required. In such cases, one usually desires, inter alia, an accurate calculation of the particle distribution functions in velocity space. However, velocity space diffusion affects most, perhaps all, kinetic simulations to some degree, leading to numerical thermalization, and consequently distortion of the velocity distribution functions, among other undesirable effects. The rate of such thermalization can be considered a figure of merit for kinetic simulations. This paper shows that, contrary to previous assumption, the addition of Monte Carlo collisions to a one-dimensional particle-in-cell simulation seriously degrades certain properties of the simulation. In particular, the thermalization time can be reduced by as much as three orders of magnitude. This effect makes obtaining a strictly converged simulation results difficult in many cases of practical interest. * Electronic address: miles.turner@dcu.ie

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Section: Introductionmentioning

confidence: 99%

Kinetic properties of particle-in-cell simulations compromised by Monte Carlo collisions

Turner

2006

Physics of Plasmas

103

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“…One of the drawbacks of using a finite-difference scheme is summed up by the Courant-Friedrichs-Levy (CFL) criterion. It states that the fastest moving particles only travel a small fraction of the mesh spacing in a timestep [21]. In this work the electric field is unchanged throughout the simulation.…”

Section: Introductionmentioning

confidence: 99%

Convective scheme solution of the Boltzmann transport equation for nanoscale semiconductor devices

Fixel

Hitchon

2007

Journal of Computational Physics

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“…Hitchon et al [14][15][16] used the example of a two-dimensional phase space (z, v) as an example for the sake of simplicity in explaining the scheme. At each time step the geometric center of the cell to which the value of the phase density of the volume of the given cell was ascribed is shifted according to prescribed equations of motion (the equations of the characteristics of the kinetic equations).…”

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confidence: 99%

“…This scheme is most effective in cases in which convection prevails over diffusion. A detailed description of the convective scheme is presented in [15]. The scheme was later applied to different transport equations in different regions of the physics of gas discharge, plasma chemistry, and so forth.…”

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confidence: 99%

“…The results of numerical simulation of the distribution function of the ions in the sheath region are given in [15] as an illustrative example of the application of the convective scheme. In this example the distribution function obtained by Emmert et al [18] was prescribed on the left-hand (plasma) boundary of the region of computation, while for the electrons the Boltzmann relation was assumed to hold.…”

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confidence: 99%

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Application of the particle-in-cell method for numerical simulation of sheath plasma

Filippychev¹

1998

Comput Math Model

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We give a survey of papers on the numerical simulation of the sheath plasma using the particle-in-cell method. We study the problem of the behavior of a plasma bounded in the longitudinal direction of an absorbing wall. The model studied contains charged particles (electrons and ions) 1. Introduction. Under laboratory conditions a plasma is always bounded by surfaces of a suitable device. The study of the processes in the sheath layer occupies a significant place in the studies of plasma physics. The importance of this problem is due to the large number of different applications among which one may mention electrostatic probes, divertor and limiter tokamak plates, thermoemission energy transformers, plasma electrons, and ion particle sources, plasma technology processes, and so forth.In the present paper we study a one-dimensional plasma model consisting of electrons and single-charge ions. In the longitudinal direction the system is bounded by absorbing walls. Due to their greater mobility the electron flux across any section of plasma is so much larger than the ion flux that the condition of approximately equal exit of electrons and ions from the plasma region (the condition of steady state of the system) leads to a plasma potential that is positive relative to the walls. The electrostatic potential varies only weakly in the plasma region, where the ion and electron densities are approximately equal (quasi-neutrality of the plasma). Near the absorbing surface a region approximately several Debye lengths in extent forms, in which the quasi-neutrality of the plasma is significantly violated, and in which a sharp potential drop occurs. The electric field is significantly different from null in this sheath region, which is called the Langmuir (or Debye) region.The basic problem in the theoretical study of a plasma with bounding walls is the study of the very complicated structure of the sheath regions, which to a significant degree is determined (in the absence of an external magnetic field) by the Knudsen number Kn -L/L and the Debye number De =-~.JL. Here ~. is the effective length of free travel of particles, ~-o is the Debye length, and L is the characteristic macroscopic dimension of the problem (the length of the region). A case of practical interest is the case Kn << 1, De << 1. Here the region containing the charged particles can be divided into a quasi-neutral hydrodynamic part and a thin sheath layer of bulk charge. Usually in a gas-discharge plasma the inequalities L >> L >> L D hold. In this case a collisionless protective layer forms around the absorbing wall, to which the strongly nonequilibrium quasi-neutral Knudsen layer is adjacent. Depending on the problem in question we use different models for describing the plasma. Far away from the wall (at distances that exceed several free travel lengths) the plasma is quasi-neutral and collisional, and the distribution function of the velocities of the particles is nearly Maxwell. In this region we use hydrodynamic models or the diffusion approximation to...

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An efficient scheme for convection-dominated transport

Cited by 65 publications

References 12 publications

Kinetic properties of particle-in-cell simulations compromised by Monte Carlo collisions

Kinetic properties of particle-in-cell simulations compromised by Monte Carlo collisions

Convective scheme solution of the Boltzmann transport equation for nanoscale semiconductor devices

Application of the particle-in-cell method for numerical simulation of sheath plasma

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