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21. The Discrete Equations
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Boundary Conditions
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Finite Difference Equations
XII.
Finite Difference Equations
21. The Discrete Equations
21.1 Time and Space discretizations
21.1.1 Averaging operators
21.1.2 Derivative operators
21.2 Key to understanding finite difference equations
21.2.1 Rules for manipulating operators
21.2.2 Rules involving summations
21.2.3 Other rules
21.3 Primitive finite difference equations
21.3.1 Momentum equations
21.3.2 Tracer equations
21.4 Time Stepping Schemes
21.4.1 Leapfrog
21.4.2 Forward
21.4.3 Euler Backward
21.4.4 Robert time filter
22. Solving the Discrete equations
22.1
Start of computation within Memory Window
22.2 loadmw (load the memory window)
22.2.1 Land/Sea masks
22.2.2 Reading latitude rows into the Memory window
22.2.3 Constructing the total velocity
22.2.4 Computing quantities within the memory window
22.2.4.1 Example 1: density
22.2.4.2 Example 2: Advective velocity on the eastern face of T-cells
22.2.4.3 Example 3: Advective velocity on the bottom face of U-cells
22.3 adv_vel (computes advective velocities)
22.3.1 Advective velocities for T cells
22.3.2 Advective velocities for U cells
22.3.3 Vertical velocity on the ocean bottom
22.3.3.1 Summary of the continuum results
22.3.3.2 Discrete vertical velocity at the ocean bottom
22.4 isopyc (computes isoneutral mixing tensor components)
22.5 vmixc (computes vertical mixing coefficients)
22.6 hmixc (computes horizontal mixing coefficients)
22.7 setvbc (set vertical boundary conditions)
22.8 tracer (computes tracers)
22.8.1 Tracer components
22.8.2 Advective and Diffusive fluxes
22.8.3 Isoneutral fluxes
22.8.4 Source terms
22.8.5 Sponge boundaries
22.8.6 Shortwave solar penetration
22.8.7 Tracer operators
22.8.7.1 Implicit vertical diffusion
22.8.7.2 Isoneutral mixing
22.8.7.3 Gent-McWilliams advection velocities
22.8.8 Solving for the tracer
22.8.8.1 Explicit vertical diffusion
22.8.8.2 Implicit vertical diffusion
22.8.9 Diagnostics
22.8.10 End of tracer components
22.8.11 Explicit Convection
22.8.12 Filtering
22.8.13 Accumulating
22.9 baroclinic (computes internal mode velocities)
22.9.1 Hydrostatic pressure gradient terms
22.9.2 Momentum components
22.9.3 Advective and Diffusive fluxes
22.9.4 Source terms
22.9.5 Momentum operators
22.9.5.1 Coriolis treatment
22.9.6 Solving for the time derivative of velocity
22.9.6.1 Explicit vertical diffusion
22.9.6.2 Implicit vertical diffusion
22.9.7 Diagnostics
22.9.8 Vertically averaged time derivatives of velocity
22.9.9 End of momentum components
22.9.10 Computing the internal modes of velocity
22.9.10.1 Explicit Coriolis treatment
22.9.10.2 Semi-implicit Coriolis treatment
22.9.11 Filtering
22.9.12 Accumulating
22.10
End of computation within Memory Window
22.11 barotropic (computes external mode velocities)
22.12 diago
RC Pacanowski and SM Griffies, GFDL, Jan 2000
