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Lax-Wendroff and McCormack Schemes for Numerical Simulation of Unsteady Gradually and Rapidly Varied Open Channel Flow

Machalińska-Murawska J., Szydłowski M.

Archives of Hydro-Engineering and Environmental Mechanics

2013

Vol. 60, nr 1-4

51--62

Two explicit schemes of the finite difference method are presented and analyzed in the paper. The applicability of the Lax-Wendroff and McCormack schemes for modeling unsteady rapidly and gradually varied open channel flow is investigated. For simulation of the transcritical flow the original and improved McCormack scheme is used. The schemes are used for numerical solution of one dimensional Saint-Venant equations describing free surface water flow. Two numerical simulations of flow with different hydraulic characteristics were performed – the first one for the extreme flow of the dam-break type and the second one for the simplified flood wave propagation problem. The computational results are compared to each other and to arbitrary solutions.

Numerical Simulation of Transient Flow in Storm Sewers Using Standard and Improved McCormack Scheme

Szydłowski M., Machalińska-Murawska J.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2012

Vol. 16, No 1-2

53-74

This paper describes the results of the first part of the research project which aims at developing a hydraulic model for simulation of unsteady flows in storm sewers ranging from gravity flows to surcharged flows resulting with water outflow on the ground surface and propagation of inundation in the flooded area. The paper focuses on the development and assessment of a second-order explicit numerical scheme for unsteady flows in sewers, but only in a single pipe at this moment, without any special elements such as manholes or drop shafts and with no water overflowing problem. The problem of water flow in sewer system pipes is associated with some specific phenomena occurring in conduits during storm events. If the pipes start to be fully filled with water, there is a transition from free surface to pressurized flow. Then, the vice versa effect can be observed. Such transitions are also possible in sewers when the discharge is controlled by control devices, such as gates for example. Moreover, the rapidly varied flow with some hydraulic local effects such as hydraulic jumps or bores can appear during extreme rain episodes. The appropriate modeling techniques have to be applied to solve these problems. The ‘Preissmann slot’ concept is implemented to simulate the pressurized flow. The original and improved McCormack scheme is used for transcritical flow simulation. The calculated results obtained for some benchmark tests are compared with numerical solutions and laboratory measurements published in the technical literature.