1. Simulate shallow water equation on matlab in 1-D for a channel by using the suitable finite differencing scheme. Free surface flows common in Hydraulics are usually described by means of the shallow water equations, provided that the representative vertical dimensions are small with respect to the horizontal dimensions. Despite their simplicity, this description is valid in many practical applications, rendering worthwhile the efforts in developing good numerical methods to solve the corresponding system of differential equations. The following differencing schemes would be looked into:
- Lax Wendroff scheme
- MacCormack Scheme
- Forward backward differencing
- Dam break and validation
2. Design a turbine to be placed in the simulation and calculated to power
3. Design another turbine distance away from the first turbine and calculate
the effect of the wake from the first turbine.