HAL Id: hal-00076842
https://hal.archives-ouvertes.fr/hal-00076842
Submitted on 29 May 2006
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Comparison of numerical schemes for
Fokker-Planck-Landau equation
Christophe Buet, Stéphane Cordier, Françis Filbet
To cite this version:
Christophe Buet, Stéphane Cordier, Françis Filbet. Comparison of numerical schemes for
Fokker-Planck-Landau equation. 2001, p 161-181. �hal-00076842�
1e-06 1e-05 0.0001 0.001 0.01 0.1 0 2 4 6 8 10 The quadratic error for the spectral method
32 modes 16 modes 0.0001 0.001 0.01 0.1 0 2 4 6 8 10 The quadratic error for the multigrid method
32 points 16 points 0.0001 0.001 0.01 0.1 0 2 4 6 8 10 The quadratic error for the pseudo-isotropic method
32 points 16 points -4.28 -4.26 -4.24 -4.22 -4.2 -4.18 0 2 4 6 8 10 The entropy for the spectral method
32 modes 16 modes -4.28 -4.26 -4.24 -4.22 -4.2 -4.18 0 2 4 6 8 10 The entropy for the multigrid method
32 points 16 points -4.28 -4.26 -4.24 -4.22 -4.2 -4.18 0 2 4 6 8 10 The entropy for the pseudo-isotropic method
32 points 16 points
12 13 14 15 16 0 2 4 6 8 10 t
The fourth order moment for the spectral method 32 modes 16 modes 12 13 14 15 16 0 2 4 6 8 10 t
The fourth order moment for the multigrid method 32 points 16 points 12 13 14 15 16 0 2 4 6 8 10 t
The fourth order moment for the pseudo-isotropic method 32 points 16 points -0.0222 -0.022 -0.0218 -0.0216 -0.0214 -0.0212 -0.021 -0.0208 -0.0206 -0.0204 0 50 100 150 200 250 300 Evolution of the entropy for the spectral method
Spectral code - 16 modes 1D isotropic code -0.0222 -0.022 -0.0218 -0.0216 -0.0214 -0.0212 -0.021 -0.0208 -0.0206 -0.0204 0 50 100 150 200 250 300 Evolution of the entropy for the multigrid method
multigrid code - 32 points 1D isotropic code -0.0222 -0.022 -0.0218 -0.0216 -0.0214 -0.0212 -0.021 -0.0208 -0.0206 -0.0204 0 50 100 150 200 250 300 Evolution of the entropy for the pseudo-isotropic method
pseudo-isotropic code - 32 points 1D isotropic code
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Distribution function evolution for the spectral method
t=000 t=050 t=500 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Distribution function evolution for the multigrid method
t=000 t=050 t=500 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Distribution function for the pseudo-isotropic method
t=000 t=050 t=500
0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 2 4 6 8 10 12 14 16 18 20 Temperature evolution with 16 modes
Tx(t) Ty(t) and Tz(t) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 2 4 6 8 10 12 14 16 18 20 Temperature evolution with 32 points
Tx(t) Ty(t) and Tz(t)
-9
-8
-7
-6
-5
-4
0
5
10
15
20
Entropy evolution for spectral and multigrid methods
multigrid method
spectral method
18
19
20
21
22
23
24
25
0
5
10
15
20
Fourth order moment for spectral and multigrid methods
multigrid method
spectral method
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0
1
2
3
4
5
6
Distribution function evolution for the spectral method
t=0
t=5
t=10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0
1
2
3
4
5
6
Distribution function evolution for the multigrid method
t=0
t=5
t=10
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0
20
40
60
80
100
120
140
160
180
Evolution of the temperature for test 1
Tx(t)
Ty(t) and Tz(t)
Total temperature
-6.6
-6.5
-6.4
-6.3
-6.2
-6.1
-6
-5.9
-5.8
-5.7
0
20
40
60
80
100
120
140
160
180
Evolution of the entropy for test 1
Numerical entropy
Stationary state
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -4 -3 -2 -1 0 1 2 3 4 Distribution function for the free transport
t=0.00 t=0.05 t=0.10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -4 -3 -2 -1 0 1 2 3 4 Distribution function for k=10e-3
t=0.00 t=0.05 t=0.10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -4 -3 -2 -1 0 1 2 3 4 Distribution function for k=10e-4
t=0.00 t=0.05 t=0.10
