Conservative semi-Lagrangian kinetic scheme coupled with implicit finite element field solver for multidimensional Vlasov Maxwell system

Liu, Hongtao; Cai, Xiaofeng; Lapenta, Giovanni; Cao, Yong

doi:10.1016/j.cnsns.2021.105941

Cited by 9 publications

(4 citation statements)

References 58 publications

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“…Published full Vlasov simulations of magnetic reconnection (e.g. Schmitz and Grauer [2006a], Pezzi et al [2019Pezzi et al [ , 2021, Liu et al [2021]) did not go beyond the GEM reconnection setup [Birn et al, 2001] which is computationally manageable due to the small system size.…”

Section: Introductionmentioning

confidence: 99%

An Energy Conserving Vlasov Solver That Tolerates Coarse Velocity Space Resolutions: Simulation of MMS Reconnection Events

Allmann-Rahn,

Lautenbach,

Grauer

2021

Preprint

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Vlasov solvers that operate on a phase-space grid are highly accurate but also numerically demanding. Coarse velocity space resolutions, which are unproblematic in particle-in-cell (PIC) simulations, can lead to numerical heating or oscillations in standard continuum Vlasov methods. We present a new dual Vlasov solver which is based on an established positivity preserving advection scheme for the update of the distribution function and an energy conserving partial differential equation solver for the kinetic update of mean velocity and temperature. The solvers work together via moment fitting during which the maximum entropy part of the distribution function is replaced by the solution from the partial differential equation solver. This numerical scheme makes continuum Vlasov methods competitive with PIC methods concerning computational cost and enables us to model large scale reconnection in Earth's magnetosphere with a fully kinetic continuum method. The simulation results agree well with measurements by the MMS spacecraft.

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Section: Introductionmentioning

confidence: 99%

An Energy Conserving Vlasov Solver That Tolerates Coarse Velocity Space Resolutions: Simulation of MMS Reconnection Events

Allmann-Rahn,

Lautenbach,

Grauer

2021

Preprint

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“…Fluid models are generally suitable for modeling discharge processes at high pressure. Kinetic models, including PIC/MCC methods and direct kinetic simulations [13][14][15], are necessary when the pressure decreases and the mean free path becomes longer. This method is generally only suitable for small-scale simulations because of the high computational cost and because the Debye length, cyclotron radius, and plasma oscillation frequency must be resolved.…”

Section: Introductionmentioning

confidence: 99%

Electrical characteristics of the GEC reference cell at low pressure: a two-dimensional PIC/MCC modeling study

Chen,

Wang,

et al. 2024

Plasma Sources Sci. Technol.

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The electrical characteristics of the Gaseous Electronics Conference (GEC) reference cell at low pressures are investigated using a two-dimensional electrostatic implicit particle-in-cell / Monte Carlo collision model (PIC / MCC) in cylindrical coordinates. The coupling between the complex reactor geometry and the external circuit is included via an equivalent capacitance calculated from the electric energy density and the charge conservation equation. The results of this model are compared with experimental measurements and other model calculations and show agreement. The plasma series resonance (PSR) effect, closely related to electron heating, is observed in this numerical simulation of a strongly asymmetric reactor at low pressures. The plasma kinetics of the capacitively coupled discharge and details of the external circuit response, including electrical waveforms and higher-order harmonics, are discussed at different pressures, which provides important insights for understanding the power coupling mechanisms in capacitively coupled discharges.

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“…The Vlasov equation, a 6-D nonlinear partial differential equation (PDE), provides an ab-initio description of the dynamics of such plasmas and is deemed to be the gold standard in plasma simulation. It can be solved deterministically using Eulerian [1][2][3][4][5] or semi-Lagrangian [6][7][8][9][10][11][12][13][14] grid-based methods. Unlike the alternative particle-in-cell (PIC) approach [15][16][17][18][19][20][21][22], these methods do not suffer from stochastic noise issues; however, they are extremely computationally expensive thanks to the exponential scaling of cost with respect to dimensionality and the resolution requirements stemming from the multi-scale dynamics that characterizes the vast majority of nonlinear plasma behavior.…”

Section: Introductionmentioning

confidence: 99%

A quantum-inspired method for solving the Vlasov-Poisson equations

Ye,

Loureiro

2022

Preprint

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Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently, it has been proposed that matrix product state (MPS) methods, a quantum-inspired but classical algorithm, can be used to solve partial differential equations with exponential speed-up, provided that the solution can be compressed and efficiently represented as an MPS within some tolerable error threshold. In this work, we explore the practicality of MPS methods for solving the Vlasov-Poisson equations in 1D1V, and find that important features of linear and nonlinear dynamics, such as damping or growth rates and saturation amplitudes, can be captured while compressing the solution significantly. Furthermore, by comparing the performance of different mappings of the distribution functions onto the MPS, we develop an intuition of the MPS representation and its behavior in the context of solving the Vlasov-Poisson equations, which will be useful for extending these methods to higher dimensional problems.

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Conservative semi-Lagrangian kinetic scheme coupled with implicit finite element field solver for multidimensional Vlasov Maxwell system

Cited by 9 publications

References 58 publications

An Energy Conserving Vlasov Solver That Tolerates Coarse Velocity Space Resolutions: Simulation of MMS Reconnection Events

An Energy Conserving Vlasov Solver That Tolerates Coarse Velocity Space Resolutions: Simulation of MMS Reconnection Events

Electrical characteristics of the GEC reference cell at low pressure: a two-dimensional PIC/MCC modeling study

A quantum-inspired method for solving the Vlasov-Poisson equations

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