Geodesic
A new model for shallow viscoelastic free-surface flows forced by gravity on rough inclined bottom
Sébastien Boyaval1
1 Université Paris-Est, Laboratoire d’hydraulique Saint-Venant, Ecole Nationale des Ponts et Chaussées – EDF R&D – CETMEF, 6 quai Watier, 78401 Chatou Cedex, France & MATHERIALS, INRIA Rocquencourt
ESAIM. Proceedings, Tome 45 (2014), pp. 108-117.

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A thin-layer model for shallow viscoelastic free-surface gravity flows on slippery topographies around a flat plane has been derived recently in [Bouchut-Boyaval, M3AS (23) 2013]. We show here how the model can be modified for flows on rugous topographies varying around an inclined plane. The new reduced model extends the scope of one derived in [Bouchut-Boyaval, M3AS (23) 2013]. It is one particular thin-layer model for free-surface gravity flows among many ones that can be formally derived with a generic unifying procedure. Many rheologies and various shallow flow regimes have already been treated within a single unified framework in [Bouchut-Boyaval, HAL-ENPC (00833468) 2013]. The initial full model used here as a starting point is however a little different to one used in [Bouchut-Boyaval, HAL-ENPC (00833468) 2013], although the new thin-layer model is very similar to the one derived therein. Precisely, here, the bulk dissipation (due to e.g. viscosity) is neglected from the beginning, like in [Bouchut-Boyaval, M3AS (23) 2013]. Moreover, unlike in [Bouchut-Boyaval, HAL-ENPC (00833468) 2013], we perform here numerical simulations. The interest of the extension is illustrated in a physically interesting situation where new stationary solutions exist. To that aim, the Finite-Volume method proposed in [Bouchut-Boyaval, M3AS (23) 2013] needs to be modified, with an adequate discretization of the new source terms. Interestingly, we can also numerically exhibit an apparently new kind of “roll-wave” solution.
DOI : 10.1051/proc/201445011

Sébastien Boyaval 1

1 Université Paris-Est, Laboratoire d’hydraulique Saint-Venant, Ecole Nationale des Ponts et Chaussées – EDF R&D – CETMEF, 6 quai Watier, 78401 Chatou Cedex, France & MATHERIALS, INRIA Rocquencourt 
@article{EP_2014_45_a11,
     author = {S\'ebastien Boyaval},
     title = {A new model for shallow viscoelastic free-surface flows forced by gravity on rough inclined bottom},
     journal = {ESAIM. Proceedings},
     pages = {108--117},
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     year = {2014},
     doi = {10.1051/proc/201445011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201445011/}
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Sébastien Boyaval. A new model for shallow viscoelastic free-surface flows forced by gravity on rough inclined bottom. ESAIM. Proceedings, Tome 45 (2014), pp. 108-117. doi : 10.1051/proc/201445011. http://geodesic.mathdoc.fr/articles/10.1051/proc/201445011/

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