Hyperbolic reduced model for Vlasov-Poisson equation with Fokker-Planck collision
ESAIM. Proceedings, Tome 77 (2024), pp. 213-228
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This paper proposes a reduced model to simulate the one-dimensional Vlasov-Poisson equation with the non-linear Fokker-Planck operator. The model provides the space-time dynamics of a few macroscopic quantities constructed following the Reduced Order Method (ROM) in the velocity variable: the compression is thus applied to the semi-discretization of the Vlasov equation. To gain efficiency, a Discrete Empirical Interpolation Method (DEIM) is applied to the compressed non-linear Fokker-Planck operator. The size of the resulting reduced model is chosen empirically according to the Knudsen number. Furthermore, we propose a correction to the reduced collision operator that ensures the reduced moments to satisfy an Euler-type system. Numerical simulations of the reduced model show that the model can capture the plasma dynamics in different collisional regimes and initial conditions at a low cost.
Affiliations des auteurs :
Emmanuel Franck 1 ; Ibtissem Labanni 2 ; Youssouf Nasseri 1 ; Laurent Navoret 1 ; Giuseppe Parasiliti Rantone 3 ; Guillaume Steimer 1
@article{EP_2024_77_a10,
author = {Emmanuel Franck and Ibtissem Labanni and Youssouf Nasseri and Laurent Navoret and Giuseppe Parasiliti Rantone and Guillaume Steimer},
title = {Hyperbolic reduced model for {Vlasov-Poisson} equation with {Fokker-Planck} collision},
journal = {ESAIM. Proceedings},
pages = {213--228},
year = {2024},
volume = {77},
doi = {10.1051/proc/202477213},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202477213/}
}
TY - JOUR AU - Emmanuel Franck AU - Ibtissem Labanni AU - Youssouf Nasseri AU - Laurent Navoret AU - Giuseppe Parasiliti Rantone AU - Guillaume Steimer TI - Hyperbolic reduced model for Vlasov-Poisson equation with Fokker-Planck collision JO - ESAIM. Proceedings PY - 2024 SP - 213 EP - 228 VL - 77 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/202477213/ DO - 10.1051/proc/202477213 LA - en ID - EP_2024_77_a10 ER -
%0 Journal Article %A Emmanuel Franck %A Ibtissem Labanni %A Youssouf Nasseri %A Laurent Navoret %A Giuseppe Parasiliti Rantone %A Guillaume Steimer %T Hyperbolic reduced model for Vlasov-Poisson equation with Fokker-Planck collision %J ESAIM. Proceedings %D 2024 %P 213-228 %V 77 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/202477213/ %R 10.1051/proc/202477213 %G en %F EP_2024_77_a10
Emmanuel Franck; Ibtissem Labanni; Youssouf Nasseri; Laurent Navoret; Giuseppe Parasiliti Rantone; Guillaume Steimer. Hyperbolic reduced model for Vlasov-Poisson equation with Fokker-Planck collision. ESAIM. Proceedings, Tome 77 (2024), pp. 213-228. doi: 10.1051/proc/202477213
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