A new model for shallow viscoelastic free-surface flows forced by gravity on rough inclined bottom
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.
@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},
year = {2014},
volume = {45},
doi = {10.1051/proc/201445011},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201445011/}
}
TY - JOUR AU - Sébastien Boyaval TI - A new model for shallow viscoelastic free-surface flows forced by gravity on rough inclined bottom JO - ESAIM. Proceedings PY - 2014 SP - 108 EP - 117 VL - 45 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201445011/ DO - 10.1051/proc/201445011 LA - en ID - EP_2014_45_a11 ER -
%0 Journal Article %A Sébastien Boyaval %T A new model for shallow viscoelastic free-surface flows forced by gravity on rough inclined bottom %J ESAIM. Proceedings %D 2014 %P 108-117 %V 45 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/201445011/ %R 10.1051/proc/201445011 %G en %F EP_2014_45_a11
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
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