Practical computational method of open channel unsteady flows including sub ＆ super critical flows

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The explicit scheme, proposed by Moll (1998) using the Saint Venant equations in the conservation form, is advanced toward its establishment of a practical numerical method of computing coexisting subcritical and supercritical flows through analyzing how to incorporate calculations at boundaries. The scheme suppresses spurious oscillation due to numerical errors by incorporating the flux limiter in the easier calculation algorithm. Especially, the calculations at a connection between two channels with each different slope is theoretically analyzed. A set of the finite-dirrerence equations and boundary condition gives two bifurcated relations : one is valid for flows except for critical flows and the other valid for critical flows. With these the explicit scheme becomes hopeful method of analyzing unsteady flows where a control section, a hydraulic jump, and bore are given to examine the analysis on boundary calculations. In addition, connections between two channels of different cross sections such as circular or rectangular ones, where the flows change from ordinary to another ordinary flows, are dealt with to solve the finite-difference equations, the boundary conditions, and the momentum equation proper to the connection boundary. The some computational examples are given by calculations of unsteady flows including supercritical and subcrtical flows situations and/or a bore (translatory jump) in simple and rather complicated channel systems.