Considering Bottom Curvature In
Depth-averaged Open-channel Flow
Modelling, Based On Curvilinear Coordinates
Author(s)
B. J. Dewals, S. Erpicum & M. Pirotton
Abstract
Accurately modelling open-channel flows on strongly vertically curved bottoms,
such as for instance over a spillway, is a challenge for any depth-averaged flow
model. This type of computation requires the use of axes properly inclined along
the mean flow direction in the vertical plane and a modelling of curvature
effects. The present generalized model performs such computations by means of
curvilinear coordinates in the vertical plane, enabling for instance one to simulate
within one single computation domain the flows in the upstream reservoir, over
the spillway, in the stilling basin and in the river reach downstream of a dam.
The frame of reference is chosen in such a way that one of the two curvilinear
axes follows the local bottom curvature. Hence the set of generalized shallow
water equations involves explicitly not only the channel bottom slope, but also
the channel vertical curvature and its derivative. The velocity profile is
generalized in comparison with the uniform one usually assumed in the
conventional shallow-water equations. The pressure distribution is also modified
as a function of the bottom curvature and is thus not purely hydrostatic but
accounts for effects of centrifugal forces.
This enhanced mathematical modelling framework has been implemented in a
2D finite volume model. A specific flux vector splitting technique has been
developed and demonstrated to be stable for any flow regime and any bottom
curvature. The scheme offers the advantage of being dependent only on the sign
of the bottom curvature. For a vanishing bottom curvature, the new model
converges smoothly towards the conventional shallow-water equations.
Finally, two test cases are detailed and lead to satisfactory validation results
for the new model.
Keywords: shallow-water equations, finite volume, bottom curvature.
Keywords
shallow-water equations, finite volume, bottom curvature.
Related Book
Other papers in this volume
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