High order well-balanced finite difference WENO schemes for shallow water flows along channels with irregular geometry

Xiufang Wang, Gang Li, Shouguo Qian, Jiaojiao Li and Zhen Wang

Applied Mathematics and Computation, 2019, vol. 363, issue C, -

Abstract: In this paper, we present high order finite difference weighted essentially non-oscillatory (WENO) schemes for the shallow water flows along open channels with irregular geometry and over a non-flat bottom topography. The proposed schemes maintain the well-balanced property for the still water steady state solutions, namely preserve steady state at the discrete level, when there is a exact balance between the flux gradient and the source term. Compared with the traditional shallow water equations with constant cross section, the construction of the well-balanced schemes is not a trivial work due to the effect induced by the irregular geometry of the channels. To preserve the well-balanced property, we first reformulate the source term, then propose to construct the numerical fluxes by means of a flux modification technique, and finally discrete the source term with the help of a novel source term approximation. Benchmark numerical examples are applied to validate the good performances of the resulting schemes: well-balanced property, high order accuracy, and high resolution for the discontinuous solutions.

Keywords: Shallow water flows; Cross section; Still water steady state; WENO schemes; Well-balanced (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630031930579X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:363:y:2019:i:c:12

DOI: 10.1016/j.amc.2019.124587

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().