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Mesh refinement methods in ROMS

Mesh refinement methods in ROMS. Laurent Debreu. INRIA , Grenoble, France. In collaboration with Patrick Marchesiello and Pierrick Penven ( IRD , Brest, France). Outline. Principles of mesh refinement Computational aspects Integration in the ROMS kernel Applications. Outline.

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Mesh refinement methods in ROMS

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  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. 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. 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. Principles of mesh refinement 1 G0 2 6 10 G1 3 4 5 7 8 9 11 12 13 G2 Time integration algorithm interpolation update

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

  8. Computational Aspects: the AGRIF software 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 AGRIF: Adaptive Grid Refinement In Fortran Some features: • Fortran 77/90, 1D/2D/3D refinement, Staggered grids, Masked fields, parallelization(MPI) • fixed and/or adaptive grids, clustering algorithm, restoring algorithm

  9. Computational aspects: ROMS_AGRIF AGRIF in ROMS: 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 • 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 » http://www.brest.ird.fr/Roms_tools

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

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

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

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

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

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

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

  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

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