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.