Shallow water flow¶
Solve the one-dimensional shallow water equations:
\[\begin{split}h_t + (hu)_x + (hv)_y & = 0 \\
(hu)_t + (hu^2 + \frac{1}{2}gh^2)_x + (huv)_y & = 0 \\
(hv)_t + (huv)_x + (hv^2 + \frac{1}{2}gh^2)_y & = 0.\end{split}\]
Here h is the depth, (u,v) is the velocity, and g is the gravitational constant.
