Computation of Open-Channel Surges and Shocks

Unsteady flows in fixed-bed open channels have been computed for a number of years on the basis of the same assumptions as those which had previously underlain calculation of steady, gradually varied flow, the key one being hydrostatic pressure distribution in every cross-section. The St. Venant equations comprising the equations of motion and continuity for this case commonly are solved either by the method of characteristics or by finite differences in a rectangular network in the x-t plane. Positive waves are characterized by converging characteristics; once these intersect a bore or shock forms, and many customary methods of solution fail. The equations of motion for flow with and without shocks are compared, the generation of bores is analyzed by exact solution of characteristic equations, and several numerical schemes are presented for computation of unsteady flows that may contain shock zones. Comparison is made between computed results and experimental data gathered for a variety of cases; corroboration is generally good, though computation based upon characteristics is inconsistent and generates the largest errors.