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A Finite Volume Coastal Ocean Model

A Finite Volume Coastal Ocean Model. Peter C Chu and Chenwu Fan Naval Postgraduate School Monterey, California, USA. Four Types of Numerical Models. Spectral Model (not suitable for oceans due to irregular lateral boundaries) Finite Difference (z-coordinate, sigma-coordinate, …)

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A Finite Volume Coastal Ocean Model

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  1. A Finite Volume Coastal Ocean Model Peter C Chu and Chenwu Fan Naval Postgraduate School Monterey, California, USA

  2. Four Types of Numerical Models • Spectral Model (not suitable for oceans due to irregular lateral boundaries) • Finite Difference (z-coordinate, sigma-coordinate, …) • Finite Element • Finite Volume

  3. Finite Volume

  4. Finite Volume Model • Transform of PDE to Integral Equations • Solving the Integral Equation for the Finite Volume • Flux Conservation

  5. Dynamic and Thermodynamic Equations • Continuity • Momentum • Thermodynamic

  6. Integral Equations for Finite Volume • Continuity • Momentum • Thermodynamic

  7. Time Integration of Phi-Equation

  8. Comparison Between Finite Difference (z- and sigma-coordinates) and Finite Volume Schemes

  9. Seamount Test Case

  10. Initial Conditions • V = 0 • S = 35 ppt • HT = 1000 m

  11. Known Solution • V = 0 • Horizontal Pressure Gradient = 0

  12. Evaluation • Princeton Ocean Model • Seamount Test Case • Horizontal Pressure Gradient (Finite Difference and Finite Volume)

  13. Numerics and Parameterization • Barotropic Time Step: 6 s • Baroclinic Time Step: 180 s • Delta x = Delta y = 8 km • Vertical Eddy Viscosity: Mellor-Yamada Scheme • Horizontal Diffusion: Samagrinsky Scheme with the coefficient of 0.2

  14. Error Volume Transport Streamfunction

  15. Temporally Varying Horizontal Gradient Error The error reduction by a factor of 14 using the finite volume scheme.

  16. Temporally Varying Error Velocity • The error velocity reduction by a factor of 4 using the finite volume scheme.

  17. Conclusions • Use of the finite volume model has the following benefit: (1) Computation is as simple as the finite difference scheme. (2) Conservation on any finite volume. (3) Easy to incorporate high-order schemes (4) Upwind scheme

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