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SELFE: Semi-implicit EularianLagrangian finite element model for
cross scale ocean circulation
Paper by Yinglong Zhang and Antonio Baptista
Presentation 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
continuity
Tidal force
barotropic
Vertical
viscosity
coriolis
Baroclinic
Atmospheric
Vertical and horizontal diffusion
Horizontal
viscosity
Turbulence Closure
vertical diffusion,
vertical and horizontal viscosity
dissipation
Length scale, 0.3, TKE, mixing length
Stability functions
Boundary conditions
Model
parameters
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
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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 z
Allows terrain following at shallow depths,
avoids baroclinic instability at deeper depths
Grid Prisms
w
u,v
elevation
S,T FVUM
S,T ELM
Continuity
Depth averaged momentum
Implicit terms
Explicit terms
Need to eliminate
=0
Momentum
Viscosity
Viscocity – implicit
Pressure gradient – implicit
Velocity at nodes = weighted average of velocity at side centers
Or 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
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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
velocity
SELFE
ELCIRC
Volume conservation
• River discharge through a section of the
Columbia
Plume
Demonstrates need for hybrid s-z grid
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