mesh refinement methods in roms laurent debreu inria, grenoble, france in collaboration with patrick...
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![Page 1: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/1.jpg)
Mesh refinement methods in ROMS
Laurent Debreu
INRIA, Grenoble, France
In collaboration with
Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)
![Page 2: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/2.jpg)
Outline
Principles of mesh refinement Computational aspects Integration in the ROMS kernel Applications
![Page 3: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/3.jpg)
Outline
Principles of mesh refinement Computational aspects Integration in the ROMS kernel Applications
![Page 4: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/4.jpg)
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Principles of mesh refinement
• Improve a global solution
two way (fixed or adaptive) mesh refinement
for a given computation cost
Will a multiresolution model performs better than a uniform grid model ?
• Improve a local solution
one or two way (fixed or adaptive mesh refinement)
Is it necessary to use two way nesting ?
• Improve the tracking of a particular structure
Adaptive mesh refinement
![Page 5: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/5.jpg)
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Principles of mesh refinement
Run the same model on grids with different space/time resolutions
Required for the embedding:
• A time integration algorithm
• Grid’s interactions
Required for the adaptivity:
• A refinement criterion
• An efficient grid’s initialization procedure
![Page 6: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/6.jpg)
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Principles of mesh refinement
G0
G1
G2
interpolation
1
6
543
2
11
10
987 1312
update
Time integration algorithm
![Page 7: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/7.jpg)
Outline
Principles of mesh refinement Computational aspects Integration in the ROMS kernel Applications
![Page 8: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/8.jpg)
Computational Aspects: the AGRIF software
AGRIF: Adaptive Grid Refinement In Fortran
Goal: « easy » integration of (fixed or adaptive) mesh refinement features in an existing numerical model
• automatic changes of data structures at compile time
• provides interpolation and update operators
• Fortran 77/90, 1D/2D/3D refinement, Staggered grids, Masked fields, parallelization(MPI)
• fixed and/or adaptive grids, clustering algorithm, restoring algorithm
Some features:
![Page 9: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/9.jpg)
Computational aspects: ROMS_AGRIF
http://www.brest.ird.fr/Roms_tools
AGRIF in ROMS:
• each grid has it own input file and outputs
• grid’s locations specified in AGRIF_FixedGrids.In
• works in OPENMP/MPI
• forcings, initial conditions made through the « nesting gui »
2
20 45 34 59 3 3 3
30 55 70 89 3 3 2
0
1
10 30 20 40 5 3 5
0
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Computational aspects: AGRIF in other ocean models
AGRIF in the OPA model
![Page 11: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/11.jpg)
Outline
Principles of mesh refinement Computational aspects Integration in the ROMS kernel Applications
![Page 12: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/12.jpg)
Integration in the ROMS numerical kernel: Roms: Time step, Boundary conditions
adjust to
• pre_step3D 1/ 2 1/ 2,n nu T BC on 1/ 2 1/ 2,n nu T
• step2D 1/ 2 1 1, ,n n nU U
• step3D_uv1
adjust to 1/ 2nu
1 1/ 2n n nu u t rhs
• step3D_uv2
• set_HUV2
1nu BC on 1nu
* 11
2n nu u u
adjust to *u
1 * 1/ 2( , )n n nT T t DIV u t BC on 1nT
• step3D_t
1/ 2nU
1nU
1/ 2nU
UP 1/ 2 1 1, ,n n nU U
UP 1 *,nu u
UP1nT
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Integration in the ROMS numerical kernel: barotropic mode, boundary conditions
Characteristic variables :
0 0f f c c
g gU U
H H
0
gU
H
On a western boundary :
0
gU
H
0
gU
H
is the incoming characteristic
is the outgoing characteristic
0 0f f upwind upwind
g gU U
H H
0
1
2f c upwind c upwind
gU U U
H
(at speed )0 0U gH
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Integration in the ROMS numerical kernel: barotropic mode
• One way
Enforces volume conservation :*
U Uc f
f f c fU U U U
• Two – way : , (no free surface update) Uf
c fU U
(including boundary points)
Update area
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Integration in the ROMS numerical kernel: 3D velocities
3D :
0
1ˆ ˆ ˆ( ) ( )
2f f c c upwind upwind c upwindH u H u H u gH H H
• Two – way :uf
c fu u
(including boundary points)
ˆf f fu u u
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Integration in the ROMS numerical kernel: conservation
• Let be a conserved quantity:
Define by
• At initial time :
• conservation of flux equality at fine/coarse grid interfaces
• (in one way interaction) two solutions
• correct or
• correct such that then correct
• (in two way interaction) two other solutions:
• correct
• correct (in ) such that
K
( ) 0K
uKt
K
\H hK K K
0 \ 0 0 0( ) ( ) ( ) ( ( )!)H h HK t t K t t K t t K t t
hK
K
0 0H
H h
t T t T
H h ht t t tu K u K
hu
huh H
h Hu u
hK
Hu
HK 1 1
h H
n n n n n nH H h h H HK K t u K u K
\
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Integration in the ROMS numerical kernel: 3D tracers
1 1 1, , ,( ) /n n n
c W c W f c c WT T t Flux Flux H
fc f
c
HT T
H
• Two-way:
*Uf
f f f fFlux H u T
W
At (first two) interior grid points
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Integration in the ROMS numerical kernel: topography construction
Topography and initial (tracers) fields
(1 ) Ifine HR coarseK K K
IcoarseK satisfying
,
, ,1 1
2 2
Icoarse coarse
i j
I W I E W Ecoarse coarse coarse coarse
j
K K
K K K K
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Integration in the ROMS numerical kernel: summary
• Boundary conditions
• 2D velocities : Characteristics variables method
• 3D velocities : boundary conditions consistents with 2D BC
• 3D tracers : clamped
• Update (two way)
• conservative updates (two first cells only)
• flux correction for tracers
• topography definition
• identical volume and faces area in first two cells
![Page 20: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/20.jpg)
Outline
Principles of mesh refinement Computational aspects Integration in the ROMS kernel Applications
![Page 21: Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)](https://reader035.vdocuments.us/reader035/viewer/2022062714/56649d4b5503460f94a2884e/html5/thumbnails/21.jpg)
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Applications: (One/Two way comparison)
Peru application: Coarse grid domain results
Coarse grid Run Nested Run
Surface temperature and velocites
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Applications: (One/Two way comparison)
Peru application: Fine grid domain results
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Mesh refinement methods in Roms: conclusions and perspectives
• Different applications have been done in one way nesting
• Two-way nesting shoud now be extensively tested
• « fully » two way scheme
• differents topographies on coase and fine grids
• exact conservation of volume and tracers
• Future two way developments
• Time refinement
• sponge layer on instead of
• treatment of momentum fluxes
( )f cu ufu