An asymptotic preserving scheme for the vlasov-poisson-fokker-planck system in the high field regime

Jin, Shi; Wang, Li

doi:10.1016/s0252-9602(11)60395-0

Cited by 32 publications

(44 citation statements)

References 25 publications

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“…Numerical simulation of VPFP systems was studied by several authors, see e.g. [16,33,38,42,11]. However, up to our knowledge, the numerical resolution of the high field limit has still not been studied and in particular no numerical comparisons with solutions of (2.5) are available.…”

Section: 1mentioning

confidence: 99%

Numerical High-Field Limits in Two-Stream Kinetic Models and 1D Aggregation Equations

Gosse¹,

Vauchelet²

2016

SIAM J. Sci. Comput.

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Abstract. Numerical resolution of two-stream kinetic models in strong aggregative setting is considered. To illustrate our approach, we consider an 1D kinetic model for chemotaxis in hydrodynamic scaling and the high field limit of the Vlasov-Poisson-Fokker-Planck system. A difficulty is that, in this aggregative setting, weak solutions of the limiting model blow up in finite time, therefore the scheme should be able to handle Dirac measures. It is overcome thanks to a careful discretization of the macroscopic velocity resulting of Vol'pert calculus: accordingly, a new well-balanced (WB) and asymptotic preserving (AP) numerical scheme is provided. Numerical simulations confirm a good behavior of solutions.

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Section: 1mentioning

confidence: 99%

Numerical High-Field Limits in Two-Stream Kinetic Models and 1D Aggregation Equations

Gosse¹,

Vauchelet²

2016

SIAM J. Sci. Comput.

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“…In order to investigate the linear response of the Wigner-Poisson equations, we expand the distribution function and the potential around the equilibrium solution f = f 0 (v), φ = 0: 17) and then neglect second order terms. Further, we assume that the perturbed quantities can be expanded in a Fourier series both in space and in time, i.e.…”

Section: Linear Stability Analysismentioning

confidence: 99%

“…Other asymptotic limits, such as the fluid limit or the high field limit, have been investigated in Refs. [4,10,8,17].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic preserving schemes for the Wigner–Poisson–BGK equations in the diffusion limit

Crouseilles¹,

Manfredi²

2014

Computer Physics Communications

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This work focusses on the numerical simulation of the Wigner-Poisson-BGK equation in the diffusion asymptotics. Our strategy is based on a "micro-macro" decomposition, which leads to a system of equations that couple the macroscopic evolution (diffusion) to a microscopic kinetic contribution for the fluctuations. A semi-implicit discretization provides a numerical scheme which is stable with respect to the small parameter ε (mean free path) and which possesses the following properties: (i) it enjoys the asymptotic preserving property in the diffusive limit; (ii) it recovers a standard discretization of the Wigner-Poisson equation in the collisionless regime. Numerical experiments confirm the good behaviour of the numerical scheme in both regimes. The case of a spatially dependent ε(x) is also investigated.

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“…These schemes become inefficient in the high field regime. Only recently, schemes efficient in the high field regime started to emerge [24,9] in the framework of a symptoticpreserving (AP) schemes. The AP schemes are efficient in the asymptotic regime since the scheme preserves a discrete analogue of the asymptotic limit, so one does not need to numerically resolve the small scale of .…”

Section: Introductionmentioning

confidence: 99%

“…So far the only AP schemes for the high field regime were those developed in [24,9], in which Q(f ) is the Fokker-Planck operator. In this case one can combine the forcing term and the collision term into a divergence form, which cannot be done for other nonlocal collision operators to be studied in this paper.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic-Preserving Numerical Schemes for the Semiconductor Boltzmann Equation Efficient in the High Field Regime

Jin¹,

Wang²

2013

SIAM J. Sci. Comput.

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We present asymptotic-preserving numerical schemes for the semiconductor Boltzmann equation efficient in the high field regime. A major challenge in this regime is that there may be no explicit expression of the local equilibrium which is the main component of classical asymptoticpreserving schemes. ], our idea is to penalize the stiff collision term with a classical Bhatnagar-Gross-Krook operator-which is not the local equilibrium in the high field limit-while treating the stiff force term implicitly with the spectral method. These schemes, despite being implicit, can be inverted easily with a stability independent of the physically small parameter. We design these schemes for both nondegenerate and degenerate cases and show their asymptotic properties. We present several numerical examples to validate the efficiency, accuracy, and asymptotic properties of these schemes.

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An asymptotic preserving scheme for the vlasov-poisson-fokker-planck system in the high field regime

Cited by 32 publications

References 25 publications

Numerical High-Field Limits in Two-Stream Kinetic Models and 1D Aggregation Equations

Numerical High-Field Limits in Two-Stream Kinetic Models and 1D Aggregation Equations

Asymptotic preserving schemes for the Wigner–Poisson–BGK equations in the diffusion limit

Asymptotic-Preserving Numerical Schemes for the Semiconductor Boltzmann Equation Efficient in the High Field Regime

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