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

Moll（1998）利用守恒形式的Saint Venant方程提出的显式格式，通过分析如何在边界处合并计算，向建立计算共存亚临界和超临界流动的实用数值方法迈进。该方案通过在易于计算的算法中加入磁通限制器，抑制了由于数值误差引起的伪振荡。特别从理论上分析了不同坡度的两个通道之间的连接处的计算。一组有限差分方程和边界条件给出了两种分叉关系：一种对除临界流外的流动有效，另一种对临界流有效。在给出控制段、水跃段和孔洞来检验边界计算分析的情况下，显式格式成为分析非定常流场的一种有希望的方法。此外，还处理了两个不同截面通道（如圆形通道或矩形通道）之间的连接，其中流动从普通流动变为另一种普通流动，以求解连接边界特有的有限差分方程、边界条件和动量方程。文中给出了一些计算实例，包括在简单和相当复杂的通道系统中的非定常流动，包括超临界和亚临界流动情况和/或孔（平动跳）。

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.