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Exactly well‐balanced positivity preserving nonstaggered central scheme for open‐channel flows
Author(s) -
Dong Jian,
Fang Li Ding
Publication year - 2021
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.4871
Subject(s) - mathematics , discretization , shallow water equations , riemann solver , solver , open channel flow , current (fluid) , geometry , scheme (mathematics) , channel (broadcasting) , flow (mathematics) , mathematical analysis , mathematical optimization , finite volume method , mechanics , computer science , geology , physics , computer network , oceanography
Summary In this paper, we construct and study an exactly well‐balanced positivity‐preserving nonstaggered central scheme for shallow water flows in open channels with irregular geometry and nonflat bottom topography. We introduce a novel discretization of the source term based on hydrostatic reconstruction to obtain the exactly well‐balanced property for the still water steady‐state solution even in the presence of wetting and drying transitions. The positivity‐preserving property of the cross‐sectional wet area is obtained by using a modified “draining" time‐step technique. The current scheme is also Riemann‐solver‐free. Several classical problems of open‐channel flows are used to test these properties. Numerical results confirm that the current scheme is robust, exactly well‐balanced and positivity‐preserving.