Application of Godunov-type schemes to transient mixed flows

A robust model for simulating the simultaneous occurrence of free surface and pressurized flows is presented using the Preissmann slot approach for modeling pressurized flows. This model is capable of simulating transient flows in closed conduits ranging from free surface flows, to partly free surface-partly pressurized flows (mixed flows), to fully pressurized flows. Its robustness for simulating mixed flows is accomplished by: (1) Introducing a gradual transition between the pipe and the slot, and (2) Using a second-order Godunov-type scheme with a slope limiter to solve the governing free surface flow equations. The accuracy and robustness of the modified Preissmann model is investigated using five test cases. The results show that the proposed model accurately describes complex flow features, such as negative open channel-pressurized flow interfaces and interface reversals. The results also show that the proposed model is able to produce stable results for strong (rapid) transients at field scale where no sub-atmospheric flows occur.