Flux difference splitting for 1D open channel flow equations

An upwind finite difference scheme based on flux difference splitting is presented for the solution of the equations governing unsteady open channel hydraulics. An approximate Jacobian needed for splitting the flux differences is defined that satisfies the conditions required to construct a first-order upwind conservative discretization of the equations. Added limited second-order corrections make the resulting scheme robust and accurate for the computation of all regimes of open channel flow. Some numerical results and comparisons with other classical schemes under exacting conditions are presented.