Numerical methods for the two-dimensional Vlasov–Poisson equation in the finite Larmor radius approximation regime

Chartier, Philippe; Crouseilles, Nicolas; Zhao, Xiaofei

doi:10.1016/j.jcp.2018.09.007

Cited by 14 publications

(4 citation statements)

References 36 publications

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“…The presence of a slow time scale and a fast one which is 2π-periodic is amenable to the two-scale framework [5][6][7][8][9]14,15]. Then, we consider the two time scales as independent by introducing Z p (t, s) (resp.…”

Section: Multiscale Numerical Schemesmentioning

confidence: 99%

“…since Ûn 0 = Ûn 0 when ε = 0 (indeed, ⟨Q BGK ⟩ conserves gyromoments). This scheme is a consistent explicit first order time discretization of the gyrokinetic equation (8).…”

Section: Ap Properties Of Scheme B For the Gyrofluid Limitmentioning

confidence: 99%

“…For the two different limits, several contributions have been performed. For instance, uniformly accurate numerical schemes have been proposed for the finite Larmor radius limit in [8], using two-scale strategies developed in [5-7, 9, 14, 15]. On the other side, Asymptotic Preserving numerical schemes efficient in the hydrodynamic limit have been widely studied [10,11,17,19,24,25,27].…”

Section: Introductionmentioning

confidence: 99%

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Multiscale Numerical Schemes for the Collisional Vlasov Equation in the Finite Larmor Radius Approximation Regime

Crestetto,

Crouseilles,

Prel

2023

Multiscale Model. Simul.

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This work is devoted to the construction of multiscale numerical schemes efficient in the finite Larmor radius approximation of the collisional Vlasov equation. Following the paper of Bostan and Finot (2019), the system involves two different regimes, a highly oscillatory and a dissipative regimes, whose asymptotic limits do not commute. In this work, we consider a Particle-In-Cell discretization of the collisional Vlasov system which enables to deal with the multiscale characteristics equations. Different multiscale time integrators are then constructed and analysed. We prove asymptotic properties of these schemes in the highly oscillatory regime and in the collisional regime. In particular, the asymptotic preserving property towards the modified equilibrium of the averaged collision operator is recovered. Numerical experiments are then shown to illustrate the properties of the numerical schemes.

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Section: Multiscale Numerical Schemesmentioning

confidence: 99%

“…since Ûn 0 = Ûn 0 when ε = 0 (indeed, ⟨Q BGK ⟩ conserves gyromoments). This scheme is a consistent explicit first order time discretization of the gyrokinetic equation (8).…”

Section: Ap Properties Of Scheme B For the Gyrofluid Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiscale Numerical Schemes for the Collisional Vlasov Equation in the Finite Larmor Radius Approximation Regime

Crestetto,

Crouseilles,

Prel

2023

Multiscale Model. Simul.

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“…In the design of well-adapted numerical schemes to capture the slow part of the dynamics with a rather coarse discretization (compared to the fast scales), one could mention the two-scale convergence method [18,19], the micro-macro decomposition in [6], lifting with multiple time variables [8,9,10,4], exponential integrators [16,17], frequency filtering [21], and implicit-explicit time discretizations [12,13,36]. The reader is also referred to [5,7] for some numerical comparisons, including comparisons with more standard methods.…”

mentioning

confidence: 99%

Convergence Analysis of Asymptotic Preserving Schemes for Strongly Magnetized plasmas

Filbet¹,

Rodrigues²,

Zakerzadeh³

2020

Preprint

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The present paper is devoted to the convergence analysis of a class of asymptotic preserving particle schemes [Filbet & Rodrigues, SIAM J. Numer. Anal., 54(2) (2016):1120-1146 for the Vlasov equation with a strong external magnetic field. In this regime, classical Particle-In-Cell (PIC) methods are subject to quite restrictive stability constraints on the time and space steps, due to the small Larmor radius and plasma frequency. The asymptotic preserving discretization that we are going to study removes such a constraint while capturing the large-scale dynamics, even when the discretization (in time and space) is too coarse to capture fastest scales. Our error bounds are explicit regarding the discretization, stiffness parameter, initial data and time.

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Convergence analysis of asymptotic preserving schemes for strongly magnetized plasmas

2021

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Numerical methods for the two-dimensional Vlasov–Poisson equation in the finite Larmor radius approximation regime

Cited by 14 publications

References 36 publications

Multiscale Numerical Schemes for the Collisional Vlasov Equation in the Finite Larmor Radius Approximation Regime

Multiscale Numerical Schemes for the Collisional Vlasov Equation in the Finite Larmor Radius Approximation Regime

Convergence Analysis of Asymptotic Preserving Schemes for Strongly Magnetized plasmas

Convergence analysis of asymptotic preserving schemes for strongly magnetized plasmas

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