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A fast Godunov method for the water‐hammer problem
Author(s) -
Hwang YaoHsin,
Chung NienMien
Publication year - 2002
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.372
Subject(s) - water hammer , riemann solver , riemann problem , piping , godunov's scheme , mathematics , dimensionless quantity , solver , mechanics , shock tube , computational fluid dynamics , roe solver , numerical analysis , riemann hypothesis , mathematical analysis , mathematical optimization , physics , shock wave , finite volume method , thermodynamics
An efficient Godunov‐type numerical method with second‐order accuracy was developed to simulate the water‐hammer problem in piping. The exact solutions of the Riemann problem were analysed and illustrated on the intriguing solution diagram by properly introducing dimensionless variables within reasonably practical ranges. Based on the solution diagram, an efficient fast Riemann solver was also developed. Moreover, small perturbation analysis was performed to demonstrate the relations between the primitive variables, velocity and pressure, for the Riemann problem. The typical shock‐tube problem and the water‐hammer problem were implemented as sample ones to test the numerical method. It was shown that the present numerical method incorporated with Van Leer's flux limiter is a promising one to simulate fluid transient problem for piping in the present study. Copyright © 2002 John Wiley & Sons, Ltd.