A reliable second-order hydrostatic reconstruction for shallow water flows with the friction term and the bed source term

A second-order hydrostatic reconstruction (HR) scheme for the shallow water equations with a non-flat bottom topography and a Manning friction is presented. The framework of our reconstruction was from Chen and Noelle (2017). We extend it from first-order to second-order accuracy. The new second-ord...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2020-10, Vol.376, p.112871, Article 112871
Main Authors: Dong, Jian, Li, Ding Fang
Format: Article
Language:English
Subjects:
Friction source term
New hydrostatic reconstruction
Positivity preserving
Saint-Venant system
Well-balancing
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Summary:A second-order hydrostatic reconstruction (HR) scheme for the shallow water equations with a non-flat bottom topography and a Manning friction is presented. The framework of our reconstruction was from Chen and Noelle (2017). We extend it from first-order to second-order accuracy. The new second-order HR scheme endows with a new implicit method, which is used to cope with the friction term, can exactly preserve the physical relevant steady-state solutions and maintain the positivity of the water depth. Finally, we use several classical numerical experiments to test these properties of the new scheme and use experimental data to be used to compare with the numerical result. In all these numerical experiments, the new scheme produces satisfactory results.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2020.112871