A new model for shallow viscoelastic free-surface flows forced by gravity on rough inclined bottom
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 ar...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2014-09-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | http://dx.doi.org/10.1051/proc/201445011 |
| _version_ | 1828078358349479936 |
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| author | Boyaval Sébastien |
| author_facet | Boyaval Sébastien |
| author_sort | Boyaval Sébastien |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T02:46:00Z |
| format | Article |
| id | doaj.art-eea55465505240b482fb19700408af03 |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T02:46:00Z |
| publishDate | 2014-09-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-eea55465505240b482fb19700408af032023-01-02T18:01:45ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592014-09-014510811710.1051/proc/201445011proc144511A new model for shallow viscoelastic free-surface flows forced by gravity on rough inclined bottomBoyaval Sébastien0Université Paris-Est, Laboratoire d’hydraulique Saint-Venant, Ecole Nationale des Ponts et Chaussées – EDF R&D – CETMEFA 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.http://dx.doi.org/10.1051/proc/201445011 |
| spellingShingle | Boyaval Sébastien A new model for shallow viscoelastic free-surface flows forced by gravity on rough inclined bottom ESAIM: Proceedings and Surveys |
| title | A new model for shallow viscoelastic free-surface flows forced
by gravity on rough inclined bottom |
| title_full | A new model for shallow viscoelastic free-surface flows forced
by gravity on rough inclined bottom |
| title_fullStr | A new model for shallow viscoelastic free-surface flows forced
by gravity on rough inclined bottom |
| title_full_unstemmed | A new model for shallow viscoelastic free-surface flows forced
by gravity on rough inclined bottom |
| title_short | A new model for shallow viscoelastic free-surface flows forced
by gravity on rough inclined bottom |
| title_sort | new model for shallow viscoelastic free surface flows forced by gravity on rough inclined bottom |
| url | http://dx.doi.org/10.1051/proc/201445011 |
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