Author(s): Alessandro Del Piero; Maria Kazolea; Andrea G. Filippini
Linked Author(s):
Keywords: Shallow water; Discontinuous Galerkin; Subcells; High order scheme; Wet/dry interface
Abstract: In the context of urban flooding applications high-order numerical schemes for free surface flows face big numerical issues simultaneously, as they must preserve motionless steady states over complex and varying bathymetries (the well-balanced property), keep mass conservation and water height positivity in the presence of wet/dry interfaces. In order to handle these problems, it is a common practice to decrease the order of the scheme on the wet/dry fronts. In this work, we make use of the subcell technique to improve the wet/dry treatment on a higher order DG discretisation for the nonlinear shallow water equations as to better capture flooding and drying phenomena [2]. This work aims to improve the wet/dry handling within a high-order DG discretization of the nonlinear shallow water equations, allowing for more accurate modeling of flooding and drying processes [2].We propose a new subcell geometry finite volume approach embedded within the DG framework for the shallow water equations with variable bottom topography. In our method, finite volume subcells are introduced inside nearly dry DG elements to enhance the resolution of the wet/dry interface. These subcells—organized into a set of hexagonal control volumes—allow the application of a robust finite volume scheme for local wet/dry capturing. Furthermore, the theoretical framework ensuring positivity preservation and well-balancing in DG methods is extended to the proposed hybrid DG–finite volume scheme, building upon the results presented in [1]. A comparison between different geometric subcell subdivision strategies reported in the literature for unstructured triangular meshes will also be conducted, in order to investigate how the new subdivision technique affects the numerical results. The implementation and numerical tests will be performed using the C++ Aerosol library and Uhaina [3]. This work is a part of the WP3 urban flooding of the MSCA Rescuer Project [4].
Year: 2026