A structure and asymptotic preserving scheme for the quasineutral limit of the Vlasov-Poisson system
Abstract
In this work, we propose a new numerical method for the Vlasov–Poisson system that is both asymptotically consistent and stable in the quasineutral regime, {\it i.e.} when the Debye length λ is small compared to the characteristic spatial scale of the physical domain. Our approach consists in reformulating the Vlasov–Poisson system as a hyperbolic problem by applying a spectral expansion in the basis of Hermite functions in the velocity space and in designing a structure-preserving scheme for the time and spatial variables. Through this Hermite formulation, we establish a convergence result for the electric field toward its quasineutral limit together with explicit error estimates in λ. Following this path, we then propose a fully discrete numerical method for the Vlasov-Poisson system, inspired by the approach in \cite{abff24}, and rigorously prove that it is uniformly consistent in the quasineutral limit regime. Finally, we present several numerical simulations to illustrate the behavior of the proposed scheme. These results demonstrate the capability of our method to describe quasineutral plasmas, illustrate its stability and confirm its asymptotic preserving property.
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BibTeX
@misc{blaustein2026structure,
title = {{A structure and asymptotic preserving scheme for the quasineutral limit of the Vlasov-Poisson system}},
author = {Alain Blaustein and Giacomo Dimarco and Francis Filbet and Marie-Hélène Vignal},
howpublished = {HAL},
year = {2026},
month = nov,
url = {https://hal.science/hal-05022776v2},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A structure and asymptotic preserving scheme for the quasineutral limit of the Vlasov-Poisson system
AU - Alain Blaustein
AU - Giacomo Dimarco
AU - Francis Filbet
AU - Marie-Hélène Vignal
PY - 2026
DA - 2026/11/05
PB - HAL
UR - https://hal.science/hal-05022776v2
AB - In this work, we propose a new numerical method for the Vlasov–Poisson system that is both asymptotically consistent and stable in the quasineutral regime, {\it i.e.} when the Debye length λ is small compared to the characteristic spatial scale of the physical domain. Our approach consists in reformulating the Vlasov–Poisson system as a hyperbolic problem by applying a spectral expansion in the basis of Hermite functions in the velocity space and in designing a structure-preserving scheme for the time and spatial variables. Through this Hermite formulation, we establish a convergence result for the electric field toward its quasineutral limit together with explicit error estimates in λ. Following this path, we then propose a fully discrete numerical method for the Vlasov-Poisson system, inspired by the approach in \cite{abff24}, and rigorously prove that it is uniformly consistent in the quasineutral limit regime. Finally, we present several numerical simulations to illustrate the behavior of the proposed scheme. These results demonstrate the capability of our method to describe quasineutral plasmas, illustrate its stability and confirm its asymptotic preserving property.
ER -