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
40
100
500
1000