A coupled two-dimensional–three-dimensional hydrodynamic model for simulating flood wave evolution in reservoirs and riverbeds

The geometric scale of real reservoirs is immense, and their boundaries are intricate. Consequently, two-dimensional numerical simulations of the entire reservoir cannot accurately capture the three-dimensional flow characteristics in localized regions. Conversely, comprehensive three-dimensional simulations are often unfeasible due to the substantial computational resources they demand. This paper proposes a two-dimensional-three-dimensional coupled hydrodynamic model by combining a two-dimensional shallow water model and a three-dimensional free surface model based on the Lattice Boltzmann Method. The model introduces algorithms that establish unified requirements for computational parameters, ensure the conservation of physical quantities at the interface, and facilitate the inversion of two-dimensional data to three-dimensional formats, as well as the integration of three-dimensional data into two-dimensional formats. The model was applied to meticulously simulate the evolution of flood waves resulting from dam breaches over uneven riverbeds. Through theoretical analysis and experimental comparisons, a detailed examination of the conservation and coherence of physical quantities at the interface was conducted, thereby validating the accuracy of the proposed approach. Finally, the large-scale evolution of wave surges in a riverbed hydropower station reservoir was simulated, effectively demonstrating the capability to address practical hydrodynamic challenges. Additionally, the discussion highlights the computational savings achieved by this model relative to conventional three-dimensional simulations, establishing a foundation for its application in real-world engineering cases.