Mathematical foundations
on nonlinear dispersive waves
by Dr L. Ridgway Scott
Departments of Computer Science and Mathematics, University of ChicagoSyllabus
(1) Fundamental background in water flow and surface waves
- Navier-Stokes equations
- Free-surface problems
- Non-Newtonian flows.
(2) History and basic models in 1-D
- Relation to tsunamis
- Properties of models
- Comparison of models
(3) Numerical schemes
- Early attempts
- Changing the model
- State of the art
(4) Models in 3-D
- Model derivation-basic properties
- Relation to Euler equations(vortex blob)
- Stability results
(5) Recent results
- Numerical methods: state of the art
- Comparison of models