| Issue |
ESAIM: M2AN
Volume 52, Number 5, September–October 2018
|
|
|---|---|---|
| Page(s) | 1679 - 1707 | |
| DOI | https://doi.org/10.1051/m2an/2018032 | |
| Published online | 22 November 2018 | |
Congested shallow water model: roof modeling in free surface flow
Sorbonne Université, Université Paris-Diderot SPC, Cerema, CNRS, Inria, laboratoire Jacques-Louis Lions, LJLL, project-team ANGE,
F-75005
Paris, France
* Corresponding author: fabien.wahl@upmc.fr
Received:
12
July
2017
Accepted:
30
April
2018
We are interested in the modeling and the numerical approximation of flows in the presence of a roof, for example flows in sewers or under an ice floe. A shallow water model with a supplementary congestion constraint describing the roof is derived from the Navier-Stokes equations. The congestion constraint is a challenging problem for the numerical resolution of hyperbolic equations. To overcome this difficulty, we follow a pseudo-compressibility relaxation approach. Eventually, a numerical scheme based on a finite volume method is proposed. The well-balanced property and the dissipation of the mechanical energy, acting as a mathematical entropy, are ensured under a non-restrictive condition on the time step in spite of the large celerity of the potential waves in the congested areas. Simulations in one dimension for transcritical steady flow are carried out and numerical solutions are compared to several analytical (stationary and non-stationary) solutions for validation.
Mathematics Subject Classification: 35L65 / 76B07 / 76M12 / 35Q35 / 74F10
Key words: Shallow water equations / congested hyperbolic model / unilateral constraint / well-balanced scheme / entropic scheme
© EDP Sciences, SMAI 2018
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