1. Mesh refinement methods in ROMS Laurent Debreu INRIA, Grenoble, France In collaboration with Patrick Marchesiello and Pierrick Penven (IRD, Brest, France)

2. Outline  Principles of mesh refinement  Computational aspects  Integration in the ROMS kernel  Applications

3. Outline  Principles of mesh refinement  Computational aspects  Integration in the ROMS kernel  Applications

4. 4 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

5. 5 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

6. 6 Principles of mesh refinement G0G0 G1G1 G2G2 interpolation 1 6 543 2 11 10 9871312 update Time integration algorithm

7. Outline  Principles of mesh refinement  Computational aspects  Integration in the ROMS kernel  Applications

8. 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:

9. 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

10. 10 Computational aspects: AGRIF in other ocean models AGRIF in the OPA model

11. Outline  Principles of mesh refinement  Computational aspects  Integration in the ROMS kernel  Applications

12. Integration in the ROMS numerical kernel: Roms: Time step, Boundary conditions adjust to pre_step3D BC on step2D step3D_uv1 adjust to step3D_uv2 set_HUV2 BC on adjust to BC on step3D_t UP

13. 13 Integration in the ROMS numerical kernel: barotropic mode, boundary conditions Characteristic variables : On a western boundary : is the incoming characteristic is the outgoing characteristic (at speed )

14. 14 Integration in the ROMS numerical kernel: barotropic mode One way Enforces volume conservation : Two – way :, (no free surface update) (including boundary points) Update area

15. 15 Integration in the ROMS numerical kernel: 3D velocities 3D : Two – way : (including boundary points)

16. 16 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

17. 17 Integration in the ROMS numerical kernel: 3D tracers Two-way: At (first two) interior grid points

18. 18 Integration in the ROMS numerical kernel: topography construction Topography and initial (tracers) fields satisfying

19. 19 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

20. Outline  Principles of mesh refinement  Computational aspects  Integration in the ROMS kernel  Applications

21. 21 Applications: (One/Two way comparison) Peru application: Coarse grid domain results Coarse grid RunNested Run Surface temperature and velocites

22. 22 Applications: (One/Two way comparison) Peru application: Fine grid domain results

23. 23 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