Università degli Studi di Padova

“Including topographic effects in shallow water modeling”

Wednesday 22 May 2019, h.14:30 - Room 2BC30 - Elena Bachini (Padova, Dip. Mat.)


Shallow water equations are typically used to model fluid flows that develop predominantly along the horizontal (longitudinal and lateral) direction. Indeed, the so-called Shallow Water (SW) hypothesis assumes negligible vertical velocity components. The typical derivation of the SW equations is based on the integration of the Navier-Stokes equations over the fluid depth in combination with an asymptotic analysis enforcing the SW assumptions. In the presence of a general terrain, such as a mountain landscape, the model must be adapted to geometrical characteristics, since the bottom surface can be arbitrarily non-flat, with non-negligible slopes and curvatures.

After an introduction on the standard SW model, we will present a new formulation of the two-dimensional SW equations in intrinsic coordinates adapted to general and complex terrains, with emphasis on the influence of the geometry of the bottom on the solution. The proposed model is then discretized with a first order upwind Godunov Finite Volume scheme. We will give an overview of the numerical method and then show some results. The results indicate that it is important to take into full consideration the bottom geometry and slope even for relatively mild and slowly varying curvatures.