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  • Zhen Li,
  • jian dong,
  • YiMing Luo,
  • Min Liu,
  • Ding Fang Li
Zhen Li
Wuhan University

Corresponding Author:[email protected]

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jian dong
National University of Defense Technology College of Liberal Arts and Sciences
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YiMing Luo
Wuhan University
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Min Liu
Wuhan University
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Ding Fang Li
Wuhan University
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In this paper, we investigate a well-balanced and positive-preserving non-staggered central scheme, which has second-order accuracy on both time and spatial scales, for open channel flows with variable channel width and non-flat bottom. We perform piecewise linear reconstructions of the conserved variables and energy as well as discretize the source term using the property that the energy remains constant, so that the complex source term and the flux can be precisely balanced so as to maintain the steady state. The scheme also ensures that the cross-sectional wet area is positive by introducing a draining time-step technique. Numerical experiments demonstrate that the scheme is capable of accurately maintaining both the still steady-state solutions and the moving steady-state solutions, simultaneously. Moreover, the scheme has the ability to accurately capture small perturbations in the moving steady-state solution and avoid generating spurious oscillations. It is also capable of showing that the scheme is positive-preserving and robust in solving the dam-break problem.
30 Mar 2022Submitted to Mathematical Methods in the Applied Sciences
30 Mar 2022Submission Checks Completed
30 Mar 2022Assigned to Editor
09 Apr 2022Reviewer(s) Assigned
21 Jul 2022Review(s) Completed, Editorial Evaluation Pending
23 Jul 2022Editorial Decision: Revise Major
30 Aug 20221st Revision Received
01 Sep 2022Assigned to Editor
01 Sep 2022Submission Checks Completed
02 Sep 2022Reviewer(s) Assigned
19 Oct 2022Review(s) Completed, Editorial Evaluation Pending
20 Oct 2022Editorial Decision: Revise Major
30 Oct 20222nd Revision Received
31 Oct 2022Submission Checks Completed
31 Oct 2022Assigned to Editor
31 Oct 2022Review(s) Completed, Editorial Evaluation Pending
02 Nov 2022Reviewer(s) Assigned
07 Dec 2022Editorial Decision: Accept
Apr 2023Published in Mathematical Methods in the Applied Sciences volume 46 issue 6 on pages 7391-7412. 10.1002/mma.8976