1D Shallow Water Equations Dam Break

Solves the 1D Shallow Water equations using a choice of four finite difference schemes (Lax-Friedrichs, Lax-Wendroff, MacCormack and Adams Average). The Adams Average scheme was devised by myself (James Adams) in 2014.
Uses Dam Break conditions (initial water velocity is set to zero).

A choice of either zero gradient (water flows out of the domain) or reflective boundary conditions is given.

Plots both the water height and velocity at each iteration.

A heuristic time step is used. The simulation is halted if the time step becomes too small.

Plots a graph of the time step values once the simulation has finished.