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Merge pull request #316 from seahorce-scidac/paper
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hklion authored Dec 16, 2024
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Expand Up @@ -78,25 +78,24 @@ The density is calculated from a linear equation of state. The strength of verti
Like ROMS, REMORA uses a split-explicit time-stepping scheme, where several fast barotropic (2D) steps take place within each baroclinic (3D) update.
In the barotropic steps, the code solves depth-averaged versions of the 3D evolution equations.
These vertically-averaged solutions are used to calculate the sea surface height and vertical-mean velocity.
Full 3D equations are then evolved for for velocities and scalars.
Full 3D equations are then advanced to calculate depth-dependent velocities and scalars (temperature, salinity, etc.).
Specifically, REMORA uses the same time integration as Rutgers ROMS.
That is, each barotropic step consists of a leapfrog predictor followed by a three-time Adams-Moulton corrector.
The 3D momenta are updated with a third-order Adams-Bashforth scheme, and scalars are advanced with a leapfrog step with a trapezoidal correction.
The 3D velocities are updated with a third-order Adams-Bashforth scheme, and scalars are advanced with a leapfrog step with a trapezoidal correction.

The spatial discretization in REMORA uses the classic Arakawa C-grid with
scalar quantities at cell centers and normal velocities at cell faces.
Bathymetry and sea-surface height are defined at the centers of the cells of the 2D grid.
Horizontally, the evolution equations are discretized over a boundary-following, orthogonal curvilinear grid, specified by metric terms.
Horizontally, the evolution equations are discretized over a boundary-following, orthogonal curvilinear grid, which is specified by metric terms.
This formulation allows for grids that, for example, conform to coastlines.
Land areas can be included in the domain and are represented by masks on cell centers and edges.
Fluxes, velocities, and tracer values are set to zero where the land mask is true.
Land areas can be included in the domain and are represented by masks on cell centers and faces; fluxes, velocities, and tracer values are set to zero on land.
The advection terms may be calculated using second- through fourth-order accurate
spatial discretizations, including both centered difference and upwind
schemes.

Vertically, the domain is discretized using a stretched, terrain-following vertical coordinate.
There are the same number of vertical levels everywhere; a spatially-varying water column depth (bathymetry and sea-surface height) is captured by cells of different thickness.
Cell thicknesses are determined by a non-linear transformation function that has parameters to control the distribution of levels.
There are the same number of vertical levels everywhere in the domain; a spatially-varying water column depth (bathymetry and sea-surface height) is captured by cells of different thickness.
Cell thicknesses are determined by non-linear transformation and stretching functions that has parameters to control the distribution of levels.

### Physical Forcings and Boundary Conditions

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