Premium
TVD schemes for open channel flow
Author(s) -
Delis A. I.,
Skeels C. P.
Publication year - 1998
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/(sici)1097-0363(19980415)26:7<791::aid-fld688>3.0.co;2-n
Subject(s) - total variation diminishing , computation , open channel flow , mathematics , convergence (economics) , flow (mathematics) , shallow water equations , courant–friedrichs–lewy condition , channel (broadcasting) , mathematical optimization , algorithm , computer science , geometry , mathematical analysis , telecommunications , discretization , economics , economic growth
The Saint Venant equations for modelling flow in open channels are solved in this paper, using a variety of total variation diminishing (TVD) schemes. The performance of second‐ and third‐order‐accurate TVD schemes is investigated for the computation of free‐surface flows, in predicting dam‐breaks and extreme flow conditions created by the river bed topography. Convergence of the schemes is quantified by comparing error norms between subsequent iterations. Automatically calculated time steps and entropy corrections allow high CFL numbers and smooth transition between different conditions. In order to compare different approaches with TVD schemes, the most accurate of each type was chosen. All four schemes chosen proved acceptably accurate. However, there are important differences between the schemes in the occurrence of clipping, overshooting and oscillating behaviour and in the highest CFL numbers allowed by a scheme. These variations in behaviour stem from the different orders and inherent properties of the four schemes. © 1998 John Wiley & Sons, Ltd.