SELFE: Semi-implicit Eularian-Lagrangian finite element model for

cross scale ocean circulation

Paper by Yinglong Zhang and Antonio BaptistaPresentation by Charles Seaton

All figures from paper unless otherwise labeled

Comparison of model types

• Structured grids, FD: ROMS, POM, NCOM: Good for ocean modeling, require small timesteps, not capable of representing coastline details

• Unstructured grids, FE (previous): ADCIRC, QUODDY: Archaic, don’t solve primitive equations

• Unstructured grids, FV: UNTRIM-like models: require orthogonality, low order

SELFE: Unstructured grids, FE: higher order, does solve primitive equations, can follow coastlines

SELFE: equations

coriolis

Tidal force

Atmospheric Horizontalviscosity

Baroclinicbarotropic

Verticalviscosity

Vertical and horizontal diffusion

continuity

Turbulence Closurevertical diffusion, vertical and horizontal viscositydissipation

Length scale, 0.3, TKE, mixing length

Stability functions

Boundary conditions

Modelparameters

Vertical Boundary Condition for Momentum

Surface

Bed

Bottom boundary layer velocity

Stress in boundary layer

Continued next slide

Vertical Boundary Condition for Momentum (continued)

Constant stress

= 0

Numerical methods

• Horizontal grid: unstructured• Vertical grid: hybrid s-z• Time stepping: semi-implicit• Momentum equation and continuity equation

solved simultaneously (but decoupled)• Finite Element, advection uses ELM• Transport equation: FE, advection uses ELM or

FVUM

s-z vertical grid

Can be pure s, can’t be pure zAllows terrain following at shallow depths, avoids baroclinic instability at deeper depths

Grid Prisms

u,v

elevation

w

S,T FVUM

S,T ELM

Continuity

Depth averaged momentum

Explicit terms

Implicit terms

Need to eliminate = 0

Momentum

Viscosity

Viscocity – implicitPressure gradient – implicit

Velocity at nodes = weighted average of velocity at side centersOr use discontinuous velocities

Vertical velocity solved by FV

Baroclinic module

Transport: ELM or FVUM (element splitting or quadratic interpolation reduces diffusion in ELM)

FVUM for Temperature

Stability constraint (may force subdivision of timesteps)

Stability

From explicit baroclinic terms

From explicit horizontal viscosity

Benchmarks

• 1D convergence

• 3D analytical test

• Volume conservation test

• Simple plume generation test

1D Convergence

• With fixed grid, larger timesteps produce lower errors

• Convergence happens only with dx and dt both decreasing

• Changing gridsize produces 2nd order convergence in SELFE, but produces divergence in ELCIRC (non-orthogonal grid)

3D quarter annulus

• M2 imposed as a function of the angle

SELFE ELCIRCvelocity

Volume conservation• River discharge through a section of the

Columbia

Plume

Demonstrates need for hybrid s-z grid

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