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Technical Note

A Simple and Unified Linear Solver for Free-Surface and Pressurized Mixed Flows in Hydraulic Systems

1
School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2
Yangtze River Scientific Research Institute, Wuhan 430010, China
*
Author to whom correspondence should be addressed.
Water 2019, 11(10), 1979; https://doi.org/10.3390/w11101979
Received: 19 August 2019 / Revised: 18 September 2019 / Accepted: 19 September 2019 / Published: 23 September 2019
(This article belongs to the Special Issue Pipeline Fluid Mechanics)
A semi–implicit numerical model with a linear solver is proposed for the free-surface and pressurized mixed flows in hydraulic systems. It solves the two flow regimes within a unified formulation, and is much simpler than existing similar models for mixed flows. Using a local linearization and an Eulerian–Lagrangian method, the new model only needs to solve a tridiagonal linear system (arising from velocity-pressure coupling) and is free of iterations. The model is tested using various types of mixed flows, where the simulation results agree with analytical solutions, experiment data and the results reported by former researchers. Sensitivity studies of grid scales and time steps are both performed, where a common grid scale provides grid-independent results and a common time step provides time-step-independent results. Moreover, the model is revealed to achieve stable and accurate simulations at large time steps for which the CFL is greater than 1. In simulations of a challenging case (mixed flows characterized by frequent flow-regime conversions and a closed pipe with wide-top cross-sections), an artificial slot (A-slot) technique is proposed to cope with possible instabilities related to the discontinuous main-diagonal coefficients of the linear system. In this test, a slot-width sensitivity study is also performed, and the suitable slot-width ratio (ε) for the linear solver is suggested to be 0.05–0.1. View Full-Text
Keywords: free-surface flow; pressurized flow; mixed flow; semi–implicit; numerical model; linear solver free-surface flow; pressurized flow; mixed flow; semi–implicit; numerical model; linear solver
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MDPI and ACS Style

Hu, D.; Li, S.; Yao, S.; Jin, Z. A Simple and Unified Linear Solver for Free-Surface and Pressurized Mixed Flows in Hydraulic Systems. Water 2019, 11, 1979. https://doi.org/10.3390/w11101979

AMA Style

Hu D, Li S, Yao S, Jin Z. A Simple and Unified Linear Solver for Free-Surface and Pressurized Mixed Flows in Hydraulic Systems. Water. 2019; 11(10):1979. https://doi.org/10.3390/w11101979

Chicago/Turabian Style

Hu, Dechao; Li, Songping; Yao, Shiming; Jin, Zhongwu. 2019. "A Simple and Unified Linear Solver for Free-Surface and Pressurized Mixed Flows in Hydraulic Systems" Water 11, no. 10: 1979. https://doi.org/10.3390/w11101979

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