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Présentation des schémas d’advection (moment et traceurs) et opérateurs de viscosité/diffusion présents dans CROCO
Equations primitives Reynolds averaged
Schémas d’advection
Rappels : ordre d’un schéma
But : trouver une approximation des dérivées partielles => séries de taylor au point x
Ordre 4
Ordre 3
Ordre 2
Ordre 1
Ordre 1
Un « bon » schéma
- Stable, CFL=- Précis
- Peu dispersif- Peu diffusif
- Peu couteux
density anomaly (kilogram meter-3)
x-dimension of the grid
S-co
ordi
nate
at R
HO-p
oint
s
Gravitational Adjustment ExampleRange of density anomaly: 15.7401 to 18.2599 kilogram meter-3Range of x-dimension of the grid: -0.279297 to 286.279Range of S-coordinate at RHO-points: -0.999023 to -0.000976562Current time since initialization: 492 secondCurrent y-dimension of the grid: 1Frame 42 in File khinst_his.nc
pmar
ches
Tue
Oct
2 1
8:16
:05
2018
density anomaly (kilogram meter-3)
x-dimension of the grid
S-co
ordi
nate
at R
HO-p
oint
s
Gravitational Adjustment ExampleRange of density anomaly: 15.74 to 18.26 kilogram meter-3Range of x-dimension of the grid: -0.279297 to 286.279Range of S-coordinate at RHO-points: -0.999023 to -0.000976562Current time since initialization: 492 secondCurrent y-dimension of the grid: 1Frame 42 in File khinst_his_512_TS_VADV_SPLINES.nc
pmar
ches
Wed
Oct
3 1
3:42
:04
2018
density anomaly (kilogram meter-3)
x-dimension of the grid
S-co
ordi
nate
at R
HO-p
oint
s
Gravitational Adjustment ExampleRange of density anomaly: 15.7401 to 18.2599 kilogram meter-3Range of x-dimension of the grid: -0.279297 to 286.279Range of S-coordinate at RHO-points: -0.999023 to -0.000976562Current time since initialization: 492 secondCurrent y-dimension of the grid: 1Frame 42 in File khinst_his_WENO_512.nc
pmar
ches
Tue
Oct
2 1
8:16
:15
2018
�t <�x
Vmax<latexit sha1_base64="UQCnLyA6luFHvE3kPJvwAomaokE=">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</latexit><latexit sha1_base64="lG3N0I9yujXNNTir05NAP42aDl0=">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</latexit><latexit sha1_base64="lG3N0I9yujXNNTir05NAP42aDl0=">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</latexit><latexit sha1_base64="CAbR8W7AIqN5y2N+J51dAOteO9w=">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</latexit>
Options pour l’advection
Equation horizontal vertical
Moment 3D (UV_ADV)(+ eq W_ en NBQ)
UV_HADV_TVDUV_HADV_C2
UV_HADV_UP3 UV_HADV_C4
UV_HADV_UP5UV_HADV_C6
UV_HADV_WENO5
UV_VADV_TVDUV_VADV_C2
UV_VADV_SPLINES UV_VADV_WENO5
Traceurs
TS_HADV_UP3 TS_HADV_RSUP3
TS_HADV_C4TS_HADV_WENO5
TS_HADV_UP5TS_HADV_C6
TS_HADV_RSUP5
TS_VADV_TVDTS_VADV_C2
TS_VADV_SPLINESTS_VADV_AKIMA TS_VADV_WENO5
Moment 2D M2_HADV_UP3 M2_HADV_C2
Le problème d’advection : un problème d’interpolation
qi,j
ui+ 12 ,j
ui� 12 ,j
vi,j� 12
vi,j+ 12
Besoin d’evaluer qaux interfaces
x
y
qi,j
ui+ 12 ,j+1
vi,j+ 12
vi,j� 12
qi+1,j
vi+1,j+ 12
vi+1,j� 12
Besoin d’evaluer u et vau centre et aux coins
des mailles
x
y
MomentTraceurs
Advection horizontale
HADV_C2, HADV_UP3, HADV_C4,HADV_UP5, HADV_C6eqi� 1
2
qi�1 qiqi�2qi�3 qi+1 qi+2
ui� 12
Advection horizontale
HADV_RSUP3,HADV_RSUP5eqi� 1
2
qi�1 qiqi�2qi�3 qi+1 qi+2
ui� 12
=> Schémas Split-UP3 et Split-UP5
Propriétés des schémas linéaires
0 ⇡4
⇡2
3⇡4
⇡
k�x
0.0
0.2
0.4
0.6
0.8
1.0
Am
plifi
catio
nfa
ctor
C2UP3C4UP5C6
50�x 10�x 4�x 2�xwavelength
0 ⇡4
⇡2
3⇡4
⇡
k�x
0.0
0.2
0.4
0.6
0.8
1.0
Pha
seer
ror
C2UP3C4UP5C6
50�x 10�x 4�x 2�xwavelength
q = q0eikx�!t
<latexit sha1_base64="9LJ0RBlv2t1ATsSaieIsUR3h6lQ=">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</latexit><latexit sha1_base64="/Zl5mpySYrRVH6jMrIgG2pe0BPk=">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</latexit><latexit sha1_base64="/Zl5mpySYrRVH6jMrIgG2pe0BPk=">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</latexit><latexit sha1_base64="4idw3p8SFUD0DlfHjOz7jJXiWrE=">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</latexit>
qn = (A)nq0, we want A <= 1<latexit sha1_base64="BfxShEPXz2ACyc9SCqvi38DYOhw=">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</latexit><latexit sha1_base64="kU8fpnfkxKmOOM1gNGaUpUcAS1w=">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</latexit><latexit sha1_base64="kU8fpnfkxKmOOM1gNGaUpUcAS1w=">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</latexit><latexit sha1_base64="5S+crkDnuhkYXL8cycukYpx20bo=">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</latexit>
Interprétation différences finies vs volumes finis
Schéma UP3 classique
Pour annuler l’erreur d’ordre 2
Schéma UP3 au sens des volumes finis (ex Leonard 95)
xixi�1xi�2
xi� 12
qi
qi�2
qi�1
eqk� 12
Schémas WENO (e.g Acker et al, 2016), TS_HADV_WENO5
xixi�1xi�2
xi� 12
qi
qi�2
qi�1
eqk� 12
xi�3
qi�3
xi+1
qi+1
Pondération non linéaire entre 3 évaluations de la valeur d’interface
1. Convexité2. Propriété ENO (essentially non-oscillatory)3. 5e ordre si q(x) est lisse
1. Propriété ENO (il satisfait une contrainte Totale Variation Bounded)
2. Mais il ne préserve pas la monotonie !!!!
=> néanmoins : choix privilégié pour les traceurs biogéochmiques
x
q
8N, 9M,N�1X
j=1
|qj+1 � qj | M
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BIO_HADV_WENO5
Schémas TVD, UV_HADV_TVD
Pondération entre un upwind et un C2
1. Total Variation Diminishing => monotone2. Mais est d’ordre 1
eqi� 12
qi�1 qiqi�2qi�3 qi+1 qi+2
ui� 12
eqTV Di� 1
2= (1� ⇠)eqC2
i� 12+ ⇠eqUPW
i� 12
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⇠ = f(r)<latexit sha1_base64="7P6WH/qoHk2cWPtmYRT9//KZNnE=">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</latexit><latexit sha1_base64="KmuWTX92rh9PDOpE0t9lrZnkVJ4=">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</latexit><latexit sha1_base64="KmuWTX92rh9PDOpE0t9lrZnkVJ4=">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</latexit><latexit sha1_base64="auQVDjaZ/D9sO9UzgT8B3xsZSeg=">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</latexit>
ui� 12> 0 : eqTV D
i� 12
= qi�1 ; r =qi � qi�1
qi+1 � qi<latexit sha1_base64="4C2jDiiKaMy1oHD0MR6RLN98nOA=">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</latexit><latexit 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Termes non-linéaires (rhs3d.F)Formulation à la Lilly (1965)
UV_HADV_UP3
avec le choix de la direction de l’upwind fait en fonction de :
qi,j
ui+ 12 ,j+1
vi,j+ 12
vi,j� 12
qi+1,j
vi+1,j+ 12
vi+1,j� 12
Besoin d’evaluer u et vau centre et aux coins
des mailles
x
y
Schémas d’advection verticale : VADV_SPLINES
Les flux sont obtenus comme solution du problème tri-diagonal:
0 ⇡4
⇡2
3⇡4
⇡
k�x
0.0
0.2
0.4
0.6
0.8
1.0
Am
plifi
catio
nfa
ctor
SplinesUP5C6
50�x 10�x 4�x 2�xwavelength
0 ⇡4
⇡2
3⇡4
⇡
k�x
0.0
0.2
0.4
0.6
0.8
1.0
Pha
seer
ror
SplinesUP5C6
50�x 10�x 4�x 2�xwavelength
hk
hk+1
hk�1
⇠
�hk/2
+hk/2
qk
qk+1
qk�1
eqk� 12
eqk+ 12
q(⇠)
q(⇠) = qk +eqk+ 1
2� eqk� 1
2
hk⇠
+ 6
eqk+ 1
2+ eqk� 1
2
2� qk
!✓⇠2
h2k
� 1
12
◆
Formulation semi-implicite
V_ADV_IMP
Idée : séparer la vitesse verticale en une contribution explicite et une contributionimplicite (Shchepetkin 2015)
Configuration résolution ancien dt nouveau dt
BENGUELA (Penven et al) 25 km 6300s 7140s
OMAN (Vic et al) 2 km 160s 470s
Aucun contrôle sur les erreurs Obligation d’utiliser un schéma linéaire sur la partie explicite
Schémas C4 et « akima » (Van leer 1977)
V_ADV_C4, VADV_AKIMA
Comment choisir ???
Equation horizontal vertical
Moment 3D (UV_ADV)(+ eq W_ en NBQ)
UV_HADV_TVDUV_HADV_C2
UV_HADV_UP3 UV_HADV_C4
UV_HADV_UP5UV_HADV_C6
UV_HADV_WENO5
UV_VADV_TVDUV_VADV_C2
UV_VADV_SPLINES UV_VADV_WENO5
Traceurs
TS_HADV_UP3 TS_HADV_RSUP3
TS_HADV_C4TS_HADV_WENO5
TS_HADV_UP5TS_HADV_C6
TS_HADV_RSUP5
TS_VADV_TVDTS_VADV_C2
TS_VADV_SPLINESTS_VADV_AKIMA TS_VADV_WENO5
Moment 2D M2_HADV_UP3 M2_HADV_C2
+V_VADV_IMP +BIO_HADV_WENO + …
3920 combinaisons …
-> ne pas choisir choix robustes par défaut -> examiner les ordres sources d’erreur -> physique du pb :
positivité, échelles -> temps de calcul
En pratique
2 appels par par de temps -> réutilise (ou pas) les mêmes routines
Moment : 2 appels à rhs3d.F avec aussi:
- u_hadv_order5.h - uvhadv_tvd.h - uhdiff_order5.h
Traceurs : pre_step3d.F, step3d_t.Favec aussi :
- t3dadv_order5.h - compute_vert_tracer_fluxes.h
Mais aussi : schémas différents au prédicteur (moins cher)et au correcteurex : C6+WENO5, C4+UP3
# define PREDICTOR (traceurs) �
new /= 3 (moment)
t(nx,ny,nz,nt
u(nx,ny,nz,3)
Opérateurs visqueux et diffusion
Forme de l’opérateur visqueux (Wajsowic, 1993)
UV_VIS2 Tenseur visqueux (uv3dmix.F)
l’opérateur de viscosité est donné par
Assure :- conservation de la quantité de mouvement- conservation du moment angulaire- terme strictement dissipatif
UV_VIS4 Même logique appliquée 2 fois
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Fermeture de type Smagorinsky
UV_VIS_SMAGO, UV_VIS2
TS_DIF_SMAGO, UV_VIS2
Coefficient de viscosité turbulente
Coefficient de diffusion turbulente
Diffusion tournée (TS_MIX_ISO, TS_MIX_GEO)
TS_DIF2
TS_DIF4
TS_MIX_IMP : Method of stabilising correction
Diffusion tournée : illustration et limitations
Limitations : • Basé sur l’hypothèse faible pente• Diffusion non monotone (termes croisés)• Suppose une évolution basse fréquence des isoprènes
34.3 34.35 34.4 34.45 34.5 34.55 34.6Salinity [psu]
2
3
4
5
6
7
8
Tem
pera
ture
[Cel
sius]
SODA
ISONEUTRAL
ISOSIGMA
34.3 34.4 34.5 34.6 34.7Salinity [psu]
2
3
4
5
6
7
8
Tem
pera
ture
[Cel
sius
]
34.2 34.3 34.4 34.5 34.6Salinity [psu]
2
4
6
8
10
Tem
pera
ture
[Cel
sius
]
34.5 34.55 34.6 34.65 34.7 34.75 34.8Salinity [psu]
2
4
6
8
10
Tem
pera
ture
[Cel
sius
]
SODA
ESPCW WSPCW
WNPCWSPEW
SIG2
ISO2
En pratique
hmix_coef.F : coefficients
t3dmix.F: - t3dmix_ISO.F (isop ou geo) - t3dmix_S.F
t3dmix_tridiagonal.h
uv3dmix.F: - uv3dmix_S.F - uv3dmix_GP.F - uv3dmix4_S.F - uv3dmix4_GP.F
sur un pas d’Euler
step3d_t.F
step3d_uv2.F