| Abstract: |
| In this paper, we construct an improved well-balanced positivity preserving central-
upwind scheme for the two-dimensional Saint-Venant system of shallow water equations.
As in [Bryson et al., M2AN Math. Model. Numer. Anal., 45 (2011), 423{446], our scheme
is based on a continuous piecewise linear discretization of the bottom topography over an
unstructured triangular grid. The main new technique is a special reconstruction of the water
surface in partially flooded cells. This reconstruction is an extension of the one-dimensional
wet/dry reconstruction from [Bollermann et al., J. Sci. Comput., 56 (2013), 267{290].
The positivity of the computed water depth is enforced using the ``draining time-step tech-
nique introduced in [Bollermann et al., Commun. Comput. Phys., 10 (2011), 371{404].
The performance of the proposed central-upwind scheme is tested on a number of numerical
experiments. |
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