Well-Balanced Scheme for Modeling Open-Channel and Surcharged Flows in Steep-Slope Closed Conduit Systems

Abstract

The model presented in this paper preserves lake at rest conditions in sloped prismatic conduits. These schemes are based on the two-governing equation model in which open-channel flows are simulated using the Saint-Venant equations and pressurized flows using the compressible water hammer equations. The model in this paper preserves lake at rest conditions (horizontal still water) regardless of the conduit slope, resolves moving jump discontinuities over dry beds in sloped conduits, and resolves small perturbations from steady states, even when adjacent to dry regions. The preserving steady-state capability of this model is of particular importance in continuous long simulations when the conduits are relatively steep (