Multiple Solutions for the Riemann Problem in the Porous Shallow Water Equations

9 pages•Published: September 20, 2018

Luca Cozzolino, Raffaele Castaldo, Luigi Cimorelli, Renata Della Morte, Veronica Pepe, Giada Varra, Carmine Covelli and Domenico Pianese

Abstract

The Porous Shallow water Equations are widely used in the context of urban flooding simulation. In these equations, the solid obstacles are implicitly taken into account by averaging the classic Shallow water Equations on a control volume containing the fluid phase and the obstacles. Numerical models for the approximate solution of these equations are usually based on the approximate calculation of the Riemann fluxes at the interface between cells. In the present paper, it is presented the exact solution of the one-dimensional Riemann problem over the dry bed, and it is shown that the solution always exists, but there are initial conditions for which it is not unique. The non-uniqueness of the Riemann problem solution opens interesting questions about which is the physically congruent wave configuration in the case of solution multiplicity.

Keyphrases: bifurcation, exact solution, porous shallow water equations, riemann problem, urban hydrology

In: Goffredo La Loggia, Gabriele Freni, Valeria Puleo and Mauro De Marchis (editors). HIC 2018. 13th International Conference on Hydroinformatics, vol 3, pages 476-484.

Links:	https://easychair.org/publications/paper/t2rk
	https://doi.org/10.29007/31n4

BibTeX entry

@inproceedings{HIC2018:Multiple_Solutions_Riemann_Problem,
  author    = {Luca Cozzolino and Raffaele Castaldo and Luigi Cimorelli and Renata Della Morte and Veronica Pepe and Giada Varra and Carmine Covelli and Domenico Pianese},
  title     = {Multiple Solutions for the Riemann Problem in the Porous Shallow Water Equations},
  booktitle = {HIC 2018. 13th International Conference on Hydroinformatics},
  editor    = {Goffredo La Loggia and Gabriele Freni and Valeria Puleo and Mauro De Marchis},
  series    = {EPiC Series in Engineering},
  volume    = {3},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2516-2330},
  url       = {/publications/paper/t2rk},
  doi       = {10.29007/31n4},
  pages     = {476-484},
  year      = {2018}}

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