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![Page 1: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/1.jpg)
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
![Page 2: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/2.jpg)
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
![Page 3: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/3.jpg)
SELFE: equations
coriolis
Tidal force
Atmospheric Horizontalviscosity
Baroclinicbarotropic
Verticalviscosity
Vertical and horizontal diffusion
continuity
![Page 4: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/4.jpg)
Turbulence Closurevertical diffusion, vertical and horizontal viscositydissipation
Length scale, 0.3, TKE, mixing length
Stability functions
Boundary conditions
Modelparameters
![Page 5: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/5.jpg)
Vertical Boundary Condition for Momentum
Surface
Bed
Bottom boundary layer velocity
Stress in boundary layer
Continued next slide
![Page 6: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/6.jpg)
Vertical Boundary Condition for Momentum (continued)
Constant stress
= 0
![Page 7: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/7.jpg)
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
![Page 8: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/8.jpg)
s-z vertical grid
Can be pure s, can’t be pure zAllows terrain following at shallow depths, avoids baroclinic instability at deeper depths
![Page 9: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/9.jpg)
Grid Prisms
u,v
elevation
w
S,T FVUM
S,T ELM
![Page 10: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/10.jpg)
Continuity
![Page 11: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/11.jpg)
Depth averaged momentum
Explicit terms
Implicit terms
Need to eliminate = 0
![Page 12: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/12.jpg)
Momentum
Viscosity
Viscocity – implicitPressure gradient – implicit
Velocity at nodes = weighted average of velocity at side centersOr use discontinuous velocities
Vertical velocity solved by FV
![Page 13: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/13.jpg)
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)
![Page 14: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/14.jpg)
Stability
From explicit baroclinic terms
From explicit horizontal viscosity
![Page 15: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/15.jpg)
Benchmarks
• 1D convergence
• 3D analytical test
• Volume conservation test
• Simple plume generation test
![Page 16: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/16.jpg)
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)
![Page 17: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/17.jpg)
3D quarter annulus
• M2 imposed as a function of the angle
SELFE ELCIRCvelocity
![Page 18: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/18.jpg)
Volume conservation• River discharge through a section of the
Columbia
![Page 19: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/19.jpg)
Plume
Demonstrates need for hybrid s-z grid
![Page 20: SELFE: Semi-implicit Eularian- Lagrangian finite element model for cross scale ocean circulation Paper by Yinglong Zhang and Antonio Baptista Presentation.](https://reader031.fdocuments.in/reader031/viewer/2022032706/56649dea5503460f94ae50fc/html5/thumbnails/20.jpg)
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