AMP 640 Numerical Modeling in Applied Marine Physics

Course outline

Part 1 Numerical solution of PDE's (John Wang)

1. Finite difference methods
2. Method design, accuracy, truncation error.
3. Stability analysis and phase analysis
4. Numerical diffusion and numerical dispersion
5. Conservative and transportive properties
6. Treatment of loadings/forcings/boundary conditions.
7. Euler/lagrangian methods
8. Special topics: drying and flooding, existing ocean models, or ??
9. Method of weighted residuals
10. Finite element methods, collocation methods, boundary integral methods.
11. Interpolation functions (finite element shape functions)
12. Special topics: terrain following coordinates, radiation boundary condtions, or ??

Textbooks/handbooks:

• Lapidus and Pinder: Numerical Solution of PDEs in Science and Engineering
• Roache: Computational Fluid Dynamics

Part 2 Ocean Mixing and Turbulence (Darek Bogucki)

1. The ubiquitous nature of turbulence, its impact on all scales of processes
2. Governing equations, turbulent kinetic energy, vorticity dynamics; turbulent transports of mass and momentum; statistical description of turbulent flows,
3. Spectral dynamics;
4. Turbulence measurements
5. Elements of DNS and LES methods, sub-grid-scale parameterizations

Books:

1. Turbulence: An Introduction for Scientists and Engineers (Paperback) by P. A. Davidson, Peter Davidson
2. Turbulent Flows, by Pope