Discontinuous Galerkin Scheme for Geometrically Intrinsic Shallow Water Equations

Computational Science seminar series

Speaker: Dr Elena Bachini

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Shallow water models of geophysical flows must be adapted to geometrical characteristics in the presence of a general bottom topography with non-negligible slopes and curvatures, such as a mountain landscape. We derive a shallow water model defined intrinsically on the bottom surface and study its properties. For a fixed bed the resulting equations are characterized by non-autonomous flux functions and source terms embodying only the geometric information. Then we consider a time-dependent local coordinate system to derive the SW flow on a moving bottom surface. In this case, the source contains terms that are proportional to the state variable but not to its derivatives. From the numerical point of view, we extend an existing intrinsic first order Finite Volume scheme to 2nd order via the Discontinuous Galerkin method. Our goal is to identify fully intrinsic discrete operators that are robust, accurate and that explicitly maintain the symmetries of the geometrical formulation of SWE. We compare the schemes in terms of accuracy, stability, and robustness on simple surfaces.