Geometrically intrinsic modeling of 2D diffusive wave overland flow for coupled surface-subsurface hydrological applications
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Shallow water models of geophysical flows must be adapted to geometric characteristics in the presence of a general bottom topography with non-negligible slopes and curvatures, such as mountain landscapes. In this paper, we derive an intrinsic formulation for the diffusive wave approximation of the shallow water equations, defined on a local reference frame anchored on the bottom surface. We then derive a numerical discretization by means of a Galerkin finite element scheme intrinsically defined on the bottom surface. Simulations on several synthetic test cases show the importance of taking into full consideration the bottom geometry even for relatively mild and slowly varying curvatures.
