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PreprintCC BY 4.0HAL

Convergence of a multi-fluid scheme for the Vlasov--Poisson system

  • Mehdi Badsi
  • Nicolas Crouseilles
  • Daniel Han-Kwan
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Abstract

In this paper, we introduce a novel multi-fluid approximation scheme for the one-dimensional Vlasov-Poisson system, that is relevant for arbitrarily long time intervals. For low regularity solutions, we establish an error estimate in the Wasserstein-1 distance, obtaining a convergence rate of order O(h2/3), where h denotes the velocity grid size. This establishes the consistency, as the grid size tends to zero, between the pressureless Euler-Poisson and the Vlasov-Poisson systems. Numerical illustrations are given to illustrate the efficiency of our approach.

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Cite

BibTeXRIS
BibTeX
@misc{badsi2026convergence,
  title = {{Convergence of a multi-fluid scheme for the Vlasov--Poisson system}},
  author = {Mehdi Badsi and Nicolas Crouseilles and Daniel Han-Kwan},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18810},
  eprint = {2609.18810},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05741825v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Convergence of a multi-fluid scheme for the Vlasov--Poisson system
AU  - Mehdi Badsi
AU  - Nicolas Crouseilles
AU  - Daniel Han-Kwan
PY  - 2026
DA  - 2026/09/15
PB  - HAL
DO  - 10.48550/arxiv.2609.18810
UR  - https://hal.science/hal-05741825v1
AB  - In this paper, we introduce a novel multi-fluid approximation scheme for the one-dimensional Vlasov-Poisson system, that is relevant for arbitrarily long time intervals. For low regularity solutions, we establish an error estimate in the Wasserstein-1 distance, obtaining a convergence rate of order O(h^2/3), where h denotes the velocity grid size. This establishes the consistency, as the grid size tends to zero, between the pressureless Euler-Poisson and the Vlasov-Poisson systems. Numerical illustrations are given to illustrate the efficiency of our approach.
ER  -