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Hyperbolic reduced model for Vlasov-Poisson equation with Fokker-Planck collision
| Content Provider | Hyper Articles en Ligne (HAL) |
|---|---|
| Author | Franck, Emmanuel Lannabi, Ibtissem Nasseri, Youssouf Navoret, Laurent Parasiliti, Giuseppe Steimer, Guillaume |
| Copyright Year | 2023 |
| Abstract | 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. |
| Related Links | https://hal.science/hal-04099697/file/cemracs_fokkerplanck%281%29.pdf |
| Language | English |
| Publisher | HAL CCSD |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
