| Summary: | 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.
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