68 research outputs found
Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit
This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB)
model of plasma physics. This model consists of the pressureless gas dynamics
equations coupled with the Poisson equation and where the Boltzmann relation
relates the potential to the electron density. If the quasi-neutral assumption
is made, the Poisson equation is replaced by the constraint of zero local
charge and the model reduces to the Isothermal Compressible Euler (ICE) model.
We compare a numerical strategy based on the EPB model to a strategy using a
reformulation (called REPB formulation). The REPB scheme captures the
quasi-neutral limit more accurately
High Order Asymptotic Preserving and Classical Semi-implicit RK Schemes for the Euler-Poisson System in the Quasineutral Limit
In this paper, the design and analysis of high order accurate IMEX finite
volume schemes for the compressible Euler-Poisson (EP) equations in the
quasineutral limit is presented. As the quasineutral limit is singular for the
governing equations, the time discretisation is tantamount to achieving an
accurate numerical method. To this end, the EP system is viewed as a
differential algebraic equation system (DAEs) via the method of lines. As a
consequence of this vantage point, high order linearly semi-implicit (SI) time
discretisation are realised by employing a novel combination of the direct
approach used for implicit discretisation of DAEs and, two different classes of
IMEX-RK schemes: the additive and the multiplicative. For both the time
discretisation strategies, in order to account for rapid plasma oscillations in
quasineutral regimes, the nonlinear Euler fluxes are split into two different
combinations of stiff and non-stiff components. The high order scheme resulting
from the additive approach is designated as a classical scheme while the one
generated by the multiplicative approach possesses the asymptotic preserving
(AP) property. Time discretisations for the classical and the AP schemes are
performed by standard IMEX-RK and SI-IMEX-RK methods, respectively so that the
stiff terms are treated implicitly and the non-stiff ones explicitly. In order
to discretise in space a Rusanov-type central flux is used for the non-stiff
part, and simple central differencing for the stiff part. AP property is also
established for the space-time fully-discrete scheme obtained using the
multiplicative approach. Results of numerical experiments are presented, which
confirm that the high order schemes based on the SI-IMEX-RK time discretisation
achieve uniform second order convergence with respect to the Debye length and
are AP in the quasineutral limit
An Asymptotic Preserving and Energy Stable Scheme for the Euler-Poisson System in the Quasineutral Limit
An asymptotic preserving and energy stable scheme for the Euler-Poisson
system under the quasineutral scaling is designed and analysed. Correction
terms are introduced in the convective fluxes and the electrostatic potential,
which lead to the dissipation of mechanical energy and the entropy stability.
The resolution of the semi-implicit in time finite volume in space
fully-discrete scheme involves two steps: the solution of an elliptic problem
for the potential and an explicit evaluation for the density and velocity. The
proposed scheme possesses several physically relevant attributes, such as the
the entropy stability and the consistency with the weak formulation of the
continuous Euler-Poisson system. The AP property of the scheme, i.e. the
boundedness of the mesh parameters with respect to the Debye length and its
consistency with the quasineutral limit system, is shown. The results of
numerical case studies are presented to substantiate the robustness and
efficiency of the proposed method.Comment: 29 pages, research paper. arXiv admin note: text overlap with
arXiv:2206.0606
An Asymptotic Preserving Scheme for the Euler equations in a strong magnetic field
This paper is concerned with the numerical approximation of the isothermal
Euler equations for charged particles subject to the Lorentz force. When the
magnetic field is large, the so-called drift-fluid approximation is obtained.
In this limit, the parallel motion relative to the magnetic field direction
splits from perpendicular motion and is given implicitly by the constraint of
zero total force along the magnetic field lines. In this paper, we provide a
well-posed elliptic equation for the parallel velocity which in turn allows us
to construct an Asymptotic-Preserving (AP) scheme for the Euler-Lorentz system.
This scheme gives rise to both a consistent approximation of the Euler-Lorentz
model when epsilon is finite and a consistent approximation of the drift limit
when epsilon tends to 0. Above all, it does not require any constraint on the
space and time steps related to the small value of epsilon. Numerical results
are presented, which confirm the AP character of the scheme and its Asymptotic
Stability
Asymptotic-Preserving Particle-In-Cell method for the Vlasov-Poisson system near quasineutrality
International audienceThis paper deals with the numerical resolution of the Vlasov-Poisson system in a nearly quasineutral regime by Particle-In-Cell (PIC) methods. In this regime, classical PIC methods are subject to stability constraints on the time and space steps related to the small Debye length and large plasma frequency. Here, we propose an ``Asymptotic-Preserving" PIC scheme which is not subject to these limitations. Additionally, when the plasma period and Debye length are small compared to the time and space steps, this method provides a consistent PIC discretization of the quasineutral Vlasov equation. We perform several one-dimensional numerical experiments which provide a solid validation of the method and its underlying concepts
Numerical approximation of the Euler-Maxwell model in the quasineutral limit
International audienceWe derive and analyze an Asymptotic-Preserving scheme for the Euler-Maxwell system in the quasi-neutral limit. We prove that the linear stability condition on the time-step is independent of the scaled Debye length when . Numerical validation performed on Riemann initial data and for a model Plasma Opening Switch device show that the AP-scheme is convergent to the Euler-Maxwell solution when where is the spatial discretization. But, when , the AP-scheme is consistent with the quasi-neutral Euler-Maxwell system. The scheme is also perfectly consistent with the Gauss equation. The possibility of using large time and space steps leads to several orders of magnitude reductions in computer time and storage
Degenerate anisotropic elliptic problems and magnetized plasma simulations
This paper is devoted to the numerical approximation of a degenerate
anisotropic elliptic problem. The numerical method is designed for arbitrary
space-dependent anisotropy directions and does not require any specially
adapted coordinate system. It is also designed to be equally accurate in the
strongly and the mildly anisotropic cases. The method is applied to the
Euler-Lorentz system, in the drift-fluid limit. This system provides a model
for magnetized plasmas
Mini-Workshop: Numerics for Kinetic Equations
[no abstract available
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