Development of a Consistent and Stable Fully Implicit Moment Method for Vlasov--Ampère Particle in Cell (PIC) System

Taitano, William; Knoll, D. A.; Chacòn, Luis; Chen, Guangye

doi:10.1137/120881385

Cited by 37 publications

(50 citation statements)

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“…[15]. The method is based on a coupled, higher dimensional (HO) kinetic system and lower dimensional (LO) moment-field system.…”

Section: Holo System Of Equations For the Vlasov-ampère Systemmentioning

confidence: 99%

“…The closure required for the LO fluid moment system is provided by the HO density-normalized total stress-tensor S HO α , (2.18) and the discrete consistency term, γ HO α [15]. The purpose of the density normalization is to expose the stiff isothermal wave in the LO system [15].…”

Section: Holo System Of Equations For the Vlasov-ampère Systemmentioning

confidence: 99%

“…The purpose of the density normalization is to expose the stiff isothermal wave in the LO system [15]. In doing so, we enhance the convergence rate of the HO-LO iteration within a time step when the time step is large compared to the stiff acoustic time-scales.…”

Section: Holo System Of Equations For the Vlasov-ampère Systemmentioning

confidence: 99%

“…If such situation arises, then, over many time steps, the two systems will drift apart, leading to inaccurate solution and solver breakdown. The purpose of γ HO nu α is to enslave the discretization error of the LO system to the discretization error of the HO system [15] …”

Section: Discrete Consistency Termsmentioning

confidence: 99%

“…In this study, we put forth a modern, fully implicit method which accelerates the convergence of the nonlinearly coupled Vlasov-Ampère system. The algorithm is based on a new, discretely consistent implicit moment method (IMM) [15] for the Eulerian approach. The new IMM scheme is based on a high-order (HO) low-order (LO) nonlinear convergence acceleration method which has seen success in neutron transport [13], thermal radiation transport [14], neutral gas kinetics [12], and collisionless plasma physics (using a PIC approach [15]).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Charge-and-energy conserving moment-based accelerator for a multi-species Vlasov–Fokker–Planck–Ampère system, part I: Collisionless aspects

Taitano

Chacòn

2015

Journal of Computational Physics

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In this study, we propose a charge, momentum, and energy conserving discretization for the 1D-1V Vlasov-Ampère system of equations on an Eulerian grid. The new conservative discretization is nonlinear in nature, but can be efficiently converged with a momentbased nonlinear accelerator algorithm. We demonstrate the conservation and convergence properties of the scheme with various numerical examples, including a multi-scale ionacoustic shockwave problem.

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“…[15]. The method is based on a coupled, higher dimensional (HO) kinetic system and lower dimensional (LO) moment-field system.…”

Section: Holo System Of Equations For the Vlasov-ampère Systemmentioning

confidence: 99%

Section: Holo System Of Equations For the Vlasov-ampère Systemmentioning

confidence: 99%

Section: Holo System Of Equations For the Vlasov-ampère Systemmentioning

confidence: 99%

Section: Discrete Consistency Termsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Charge-and-energy conserving moment-based accelerator for a multi-species Vlasov–Fokker–Planck–Ampère system, part I: Collisionless aspects

Taitano

Chacòn

2015

Journal of Computational Physics

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A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials

Fatone

Funaro

Manzini

2019

Commun. Appl. Math. Comput.

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In this work, we apply a semi-Lagrangian spectral method for the Vlasov-Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the approximation of the distribution function with respect to the velocity variable. We discuss second-order accurate-in-time schemes, obtained by coupling spectral techniques in the space-velocity domain with a BDF time-stepping scheme. The resulting method possesses good conservation properties, which have been assessed by a series of numerical tests conducted on the standard two-stream instability benchmark problem. In the Hermite case, we also investigate the numerical behavior in dependence of a scaling parameter in the Gaussian weight. Confirming previous results from the literature, our experiments for different representative values of this parameter, indicate that a proper choice may significantly impact on accuracy, thus suggesting that suitable strategies should be developed to automatically update the parameter during the time-advancing procedure.

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An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov–Darwin particle-in-cell algorithm

Chen

Chacòn

2014

Computer Physics Communications

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A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen, Chacón, Barnes, J. Comput. Phys. 230 (2011) 7018). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation of Maxwell's equations, which avoids radiative aliasing noise issues by ordering out the light wave. An implicit, orbit-averaged time-space-centered finite difference scheme is applied to both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge-and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. Several 1D numerical experiments demonstrate the accuracy and the conservation properties of the algorithm. IntrodutionThe electromagnetic (EM) Particle-in-cell (PIC) method solves Vlasov-Maxwell's equations for kinetic plasma simulations [1,2]. In the standard approach, Maxwell's equations are solved on a grid, and the Vlasov equation is solved by method of characteristics using a large number of particles, from which the evolution of the probability distribution function (PDF) is obtained. The field-PDF description is tightly coupled. Maxwell's equations (or a subset thereof) are driven by moments of the PDF such as charge density and/or current density. The PDF, on the other hand, follows a hyperbolic equation in phase space, whose characteristics are determined by the fields self-consistently.To date, most PIC methods employ explicit time-stepping (e.g. leapfrog scheme), which can be very inefficient for long-time, large spatial scale simulations. The algorithmic inefficiency of standard explicit PIC is rooted in the presence of numerical stability constraints, which force both a minimum grid-size (due to the so-called finite-grid instability [1,2], which requires resolution of the smallest Debye length) and a very small timestep (due to the wellknown CFL constraint in the general electromagnetic case, c∆t < ∆x, where c is speed of

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Development of a Consistent and Stable Fully Implicit Moment Method for Vlasov--Ampère Particle in Cell (PIC) System

Cited by 37 publications

References 20 publications

Charge-and-energy conserving moment-based accelerator for a multi-species Vlasov–Fokker–Planck–Ampère system, part I: Collisionless aspects

Charge-and-energy conserving moment-based accelerator for a multi-species Vlasov–Fokker–Planck–Ampère system, part I: Collisionless aspects

A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov–Darwin particle-in-cell algorithm

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