Big Picture

1. Define a piece-wise function of initial data; do this by computing cell averages: U(i,n) = (1/delta_x)*Integral[u(x,tn)]dx evaluated over the entire cell (i.e. over flanking intercell boundaries)

2. Solve the IVP for the original conservation law, but with modified (discretized) initial data to get the solution for the next time level

3. This produces local Riemann Problems (RPs), centered on intercell boundaries.

4. Solve these local RP's, and use solution to compute fluxes