The initial data consists of a single constant state in each
of four quadrants of the x-y plane. The problem is solved in the
x-y region
and the four quadrants are given
by dividing this region by two lines
x=1/2, y=1/2.
We will use the subscripts
ll, lr, ul, urto denote lower-left, lower-right, upper-left and upper-right
quadrants respectively.
Animations of many different configurations of Riemann problems are
available here.