Implementation of Grid Nesting: a first look with grid mosaics

Implementation of Grid Nesting: a first look with grid mosaics

John Warner, USGSHernan Arango, Rutgers

Motivation slide

Existing modeling application of Hudson River.

Need to extend southern boundary into region of strong variations.

Warner, J. C., W. R. Geyer, and J. A. Lerczak (2005), Numerical modeling of an estuary: A comprehensive skill assessment, J. Geophys. Res., 110,

C05001, doi:10.1029/2004JC002691.

• Existing methods of grid manipulation• Grid nesting types• Other procedures of nesting• Development of our proposed nesting approach• Simple Application (dogbone)• Grid generation tool• Realistic Application (Hudson)

Outline

Existing methods of grid manipulation

For rectilinear grids, use manipulation techniques of:

- curvature- masking- stretching

to allow increased resolution in regions of interest.

Land/Sea masking

Grid curvature

Grid stretching

Some drawbacks of these techniques

Grid curvature in different directions

Stretching extends along entire grid

a lot of masked regions

Rectilinear grid is not ‘ideal’ to provide strong resolution along coastlines or in regions of strongly varying topography. Need methods to allow:- increased resolution in localized regions of interest- limited masking- localized curvature

Some drawbacks of these techniques

Grid curvature in different directions

Stretching extends along entire grid

a lot of masked regions

Rectilinear grid is not ‘ideal’ to provide strong resolution along coastlines or in regions of strongly varying topography. Need methods to allow:- increased resolution in localized regions of interest- limited masking- localized curvature

Need better methods: Grid Nesting (3 Types)

1) Mosaic (East-West Contact)

Grid 1 Grid 2M

1 L1

M

1

L1

1 L

M

M

1 L1

1

Grid 2Grid 1

2) Composed

1 L

M

M

1 L1

1

3) Refinement

Grid 2

Grid 1

grids aligned along one side

1 grid overlaps more than 1 boundary

localized region of increased resolution

Some issues to consider for nesting:

Need to exchange information between grids that are connected.

- Model fields are at different grid locations (Arakawa C Grid).- What needs to be exchanged ?- When do we exchange it ?- Numerical stencil of advection and mixing formulations require spatial footprint. At the grid boundaries, there are not enough points to fulfill that footprint.

Grid 1 Grid 2

What happens at the boundaries?

0 1 1 2 2 3 3

Istr = 1

Istr = 1, I_RANGE = 1 ..

FX(1,j)

FX(0,j)=FX(1,j)

Advection schemes require data fields beyond edge of the grid.

0 1 1 2 2 3 3 -2 -2 -1 -1

Periodic

Non-Periodic

For Periodic we add additional ghost points.

Nesting strategies by others

Some models exchange fluxes at boundaries

+ Use only local information.- Fluxes may be different from each grid, so need to average

them.- This will lead to different results depending on where the grids

are connected.

How do we propose to do nesting?

- For now focus on mosaic and composite grids.- For now, use coincident points (have formulation for spatial interpolation).- 2 way nested system (dynamical interaction).- Time step adjacent grids using information of the data fields from the other mesh (Ookochi, 1972).- This is similar to Periodic formulation already in ROMS- May require a dynamical interface when 2 grids are of different resolution

M

1 L1

M

1

L1

v v v v v v v v v v v v v

v v v v v v v v v v v v v

v v v v v v v v v v v v v

v v v v v v v v v v v v v

v v v v v v v v v v v v v

v v v v v v v v v v v v

uu u u u u u u u u u u

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uu u u u u u u u u u u

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L+1 L+2

Mosaic Grids: East-West Contact

Grid 1

v v v v v v v v v v v v v

uu u u u u u u u u u u

v v v v v v v v v v v v

L-1

M

1L

1

M

1

L10-1-2

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v v v v v v v v v v v v v

v v v v v v v v v v v v v

v v v v v v v v v v v v v

v v v v v v v v v v v v v

v v v v v v v v v v v v v

v v v v v v v v v v v v v

v v v v v v v v v v v v

Mosaic Grids: East-West Contact

Grid 2

v v v v v v v v v v v v

v

v

v

v

v

v

v

v

Composite grid - ROMS time stepping

main3d time loop steps for each grid sequentially, then exchange

information.

time step loop

synchronization point

Nesting.Fcall allocate_nesting

call interp_nesting

uses pointers so there is no copy of data

Pros Cons of our approachPros+ For concurrent grid spacing: results will be identical no matter how it is tiled (even with large

stencil advection schemes)+ Allows natural extension of advection schemes.+ No need to avg fluxes+ Want to only acquire primary variables from other grid. For nesting halo region currently acquire : ubar, vbar, u, v, zeta, rzeta,

Zt_avg1, DU_avg1, DV_avg1,bu/vstr, tke, gls, Akv, Akt, Huon Hvom (step3d_uv)

+ To ensure mass conservation, want to compute all secondary variables on each local grid. For nesting halo region currently compute : omega, rhoA, rhoS, rho, bvf,

Hz, z_r, z_w, Huon Hvom (set_massflux), metrics+ Greatly reduces the masked areas.

Cons- Grid is larger (depends on how you develop the grids)- Grid Preprocessing- BC's a little trickier - need to move them out of cppdefs.h

Idealized Test Case : Dogbone

Case 1: whole grid

Case 2: two separate grids

Grid 1 Grid 2

close up of connection region

-3 -2 -2 -1 -1 0 0 1 1 2 2 3 3

Lm-3 Lm-2 Lm-1 Lm L L+1 L+2

Dogbone results

Case 1: whole grid

Case 2: two separate grids

animation of free surface

Gridgen:needed for more complicated setups

1) user provides bounding polygon with identifiers for L/R turns.2) then either - nx, ny or - node coordinates3) final grids are cut out

Composite Hudson grid

Example: Hudson River Estuary + NY Harbor

free surface bottom salinity

Summary

• Developing a method for nesting the includes capabilities for mosaic grids, composite grids, and grid refinement.

• Time integration of grid points near the mesh interface is performed using data from fields of adjacent mesh.

• Simple test case (dogbone) demonstrates that the method reproduces identical results from a mosaic grid as compared to a continuous grid.

• Successful application of composite grid to a realistic estuarine setting.

• Method can be used to connect unlimited grid segments to enhance grid resolution of ROMS in regions of strongly varying coastlines.