A volume of fluid method for a two-dimensional plasma expansion problem

Thanh, K.-C. Le; Parzani, Céline; Vignal, Marie-Hélène

doi:10.1016/j.jcp.2007.02.031

Cited by 2 publications

(2 citation statements)

References 54 publications

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“…The application of this strategy to kinetic models (Vlasov-Poisson equations) has been published in [2,23,24]. The study of the transition from quasineutrality to non-quasineutrality in plasmas has been investigated in [12,15,27,28,51], as well as in [37,43,57,61]. The quasi-neutral limit has been theoretically investigated in [11,39,48,56,62].…”

Section: Plan Of These Notesmentioning

confidence: 99%

Asymptotic-Preserving Schemes for Fluid Models of Plasmas

Degond

2011

Preprint

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These notes summarize a series of works related to the numerical approximation of plasma fluid problems. We construct so-called 'Asymptotic-Preserving' schemes which are valid for a large range of values (from very small to order unity) of the dimensionless parameters that appear in plasma fluid models. Specifically, we are interested in two parameters, the scaled Debye length which quantifies how close to quasi-neutrality the plasma is, and the scaled cyclotron period, which is inversely proportional to the magnetic field strength. We will largely focus on the ideas, in order to enable the reader to apply these concepts to other situations.

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Section: Plan Of These Notesmentioning

confidence: 99%

Asymptotic-Preserving Schemes for Fluid Models of Plasmas

Degond

2011

Preprint

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“…Thus, we have to reconnect the models and follow the moving interface between quasi-neutral and non quasi-neutral zones. And, the connection of the models and the interface description are difficult problems especially in two or three dimensions, see [11], [16], [18].…”

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A Boundary Layer Problem for an Asymptotic Preserving Scheme in the Quasi-Neutral Limit for the Euler–Poisson System

Vignal¹

2010

SIAM J. Appl. Math.

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We consider the two-fluid Euler-Poisson system modeling the expansion of a quasineutral plasma in the gap between two electrodes. The plasma is injected from the cathode using boundary conditions which are not at the quasi-neutral equilibrium. This generates a boundary layer at the cathode. We numerically show that classical schemes as well as the asymptotic preserving scheme developed in [9] are unstable for general Roe type solvers when the mesh does not resolve the small scale of the Debye length. We formally derive a model describing the boundary layer. Analysing this problem, we determine well-adapted boundary conditions. These well-adapted boundary conditions stabilize general solvers without resolving the Debye length.

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A volume of fluid method for a two-dimensional plasma expansion problem

Cited by 2 publications

References 54 publications

Asymptotic-Preserving Schemes for Fluid Models of Plasmas

Asymptotic-Preserving Schemes for Fluid Models of Plasmas

A Boundary Layer Problem for an Asymptotic Preserving Scheme in the Quasi-Neutral Limit for the Euler–Poisson System

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