A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model

Alain Blaustein; Francis Filbet

Pré-Publication, Document De Travail Année : 2023

A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model

(1) , (1)

Alain Blaustein

Fonction : Auteur

Institut de Mathématiques de Toulouse UMR5219

Francis Filbet

Fonction : Auteur

Institut de Mathématiques de Toulouse UMR5219

Résumé

We propose a numerical method for the Vlasov-Poisson-Fokker-Planck model written as an hyperbolic system thanks to a spectral decomposition in the basis of Hermite functions with respect to the velocity variable and a structure preserving finite volume scheme for the space variable. On the one hand, we show that this scheme naturally preserves both stationary solutions and linearized free-energy estimate. On the other hand, we adapt previous arguments based on hypocoercivity methods to get quantitative estimates ensuring the exponential relaxation to equilibrium of the discrete solution for the linearized Vlasov-Poisson-Fokker-Planck system, uniformly with respect to both scaling and discretization parameters. Finally, we perform substantial numerical simulations for the nonlinear system to illustrate the efficiency of this approach for a large variety of collisional regimes (plasma echos for weakly collisional regimes and trend to equilibrium for collisional plasmas) and to highlight its robustness (unconditional stability, asymptotic preserving properties).

Mots clés

Hypocoercive estimates Hermite spectral method Vlasov-Poisson-Fokker-Planck

Domaines

Analyse numérique [cs.NA]

Fichier principal

paper.pdf (5.89 Mo)

paper (1).pdf (5.89 Mo)

paper.toc (1.5 Ko)

t0_f1.png (74.33 Ko)

t0_f2.png (59.77 Ko)

t0_f3.png (52.21 Ko)

t0_f6.png (42.19 Ko)

t1_f1-1.png (37.19 Ko)

t1_f1-2.png (33.21 Ko)

t1_f2-1.png (43.02 Ko)

t1_f2-2.png (28.36 Ko)

t1_f7-1.png (82.92 Ko)

t1_f7-2.png (60.2 Ko)

t1_f8-1.png (101.61 Ko)

t1_f8-2.png (68.58 Ko)

t1_f9-1.png (43.71 Ko)

t1_f9-2.png (43.71 Ko)

t1_ff0.png (148.91 Ko)

t1_ff1.png (140.91 Ko)

t1_ff2.png (141.69 Ko)

t1_ff3.png (141.31 Ko)

t1_ff4.png (141.07 Ko)

t1_ff5.png (142.35 Ko)

t2_f1-1.png (30.74 Ko)

t2_f1-2.png (30.65 Ko)

t2_f2.png (92.32 Ko)

t2_f8.png (67.71 Ko)

t2_f9.png (46.19 Ko)

t2_ff0.png (95.5 Ko)

t2_ff1.png (118.41 Ko)

t2_ff10.png (110.52 Ko)

t2_ff2.png (124.16 Ko)

t2_ff3.png (128.64 Ko)

t2_ff4.png (134.48 Ko)

t2_ff5.png (135.06 Ko)

t2_ff6.png (141.54 Ko)

t2_ff7.png (136.84 Ko)

t2_ff8.png (125.25 Ko)

t2_ff9.png (116.15 Ko)

t2_fg0.png (95.5 Ko)

t2_fg1.png (116.11 Ko)

t2_fg10.png (97.86 Ko)

t2_fg2.png (124.49 Ko)

t2_fg3.png (112.94 Ko)

t2_fg4.png (105.58 Ko)

t2_fg5.png (107.1 Ko)

t2_fg6.png (99.19 Ko)

t2_fg7.png (100.68 Ko)

t2_fg8.png (99.22 Ko)

t2_fg9.png (95.12 Ko)

t3_f3-0.png (34.77 Ko)

t3_f3-1.png (34.17 Ko)

t3_f3-2.png (26.87 Ko)

t3_f3-3.png (19.85 Ko)

t3_f8.png (43.31 Ko)

t3_f9.png (36.76 Ko)

t3_ff0.png (58.84 Ko)

t3_ff1.png (102.55 Ko)

t3_ff10.png (109.43 Ko)

t3_ff2.png (116.37 Ko)

t3_ff3.png (123.06 Ko)

t3_ff4.png (119.29 Ko)

t3_ff5.png (129.26 Ko)

t3_ff6.png (121.54 Ko)

t3_ff7.png (121.22 Ko)

t3_ff8.png (121.65 Ko)

t3_ff9.png (113.83 Ko)

t3_fg0.png (58.84 Ko)

t3_fg1.png (101.86 Ko)

t3_fg10.png (91.76 Ko)

t3_fg2.png (115.23 Ko)

t3_fg3.png (112.71 Ko)

t3_fg4.png (109.29 Ko)

t3_fg5.png (112.48 Ko)

t3_fg6.png (102.9 Ko)

t3_fg7.png (97.72 Ko)

t3_fg8.png (95.49 Ko)

t3_fg9.png (93.39 Ko)

t3_fh0.png (58.84 Ko)

t3_fh1.png (98.16 Ko)

t3_fh10.png (68.65 Ko)

t3_fh2.png (102.98 Ko)

t3_fh3.png (90.34 Ko)

t3_fh4.png (88.79 Ko)

t3_fh5.png (85.7 Ko)

t3_fh6.png (79.93 Ko)

t3_fh7.png (76.68 Ko)

t3_fh8.png (75.09 Ko)

t3_fh9.png (73.61 Ko)

Origine	Fichiers produits par l'(les) auteur(s)

Origine	Fichiers produits par l'(les) auteur(s)

Francis Filbet : Connectez-vous pour contacter le contributeur

https://hal.science/hal-04140240

Soumis le : mardi 4 juillet 2023-18:52:50

Dernière modification le : dimanche 3 décembre 2023-03:34:43

Dates et versions

hal-04140240 , version 1 (24-06-2023)

hal-04140240 , version 2 (04-07-2023)

hal-04140240 , version 3 (29-11-2023)

Licence

Paternité - Pas d'utilisation commerciale

Identifiants

HAL Id : hal-04140240 , version 2
ARXIV : 2306.14605

Citer

Alain Blaustein, Francis Filbet. A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model. 2023. ⟨hal-04140240v2⟩

Exporter

BibTeX XML-TEI Dublin Core DC Terms EndNote DataCite

127 Consultations

71 Téléchargements

A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model

Résumé

Mots clés

Domaines

Dates et versions

Licence

Identifiants

Citer

Exporter

Altmetric

Partager