Improved strategy of internal boundary conditions for levee representation in flood simulation with the 2-D shallow water modelling on unstructured grids

Accurately assessing the hydraulic influence of levees is critical for flood simulations; however, explicit representation of levee topography usually requires locally refined meshes, leading to increased computational cost in realistic applications. To address this issue, this study implements internal boundary conditions (IBCs) in an unstructured triangular-mesh finite-volume solver for the two-dimensional shallow water equations (SWEs), enabling levees to be represented as internal hydraulic discontinuities rather than explicitly resolved topographic features. To improve the original IBC formulation, characteristic-line relations are introduced to reconstruct the virtual boundary states used in the IBC flux calculation. The reconstructed boundary states provide a more consistent relation between the prescribed overtopping or breach discharge and the boundary water depth and velocity, which improves the robustness of the IBC treatment under rapidly varying levee overtopping and breaching flows. Comparisons with a locally refined numerical benchmark show that the IBC strategies can reproduce the main hydraulic effects of levee blocking, overtopping, and breach-induced floodplain inundation while reducing mesh complexity and allowing larger stable time steps. A field-scale simulation of levee-breach-induced flood propagation in the Zhangjiazhou Waterway further demonstrates the applicability of the method to complex floodplain inundation. Compared with the original IBC strategy, the improved IBC strategy provides better numerical stability and a smoother near-breach water-level response in the field-scale breach case. Overall, the proposed approach provides a physically interpretable and efficient alternative for representing levee effects in large-scale flood simulations.