Efficient and Coupled 1D-2D Hydrodynamic Framework to Model Catchment Scale Surface Flow Dynamics

Abstract Surface flow in a catchment consists of slowly varying overland flow and a predominantly fast and concentrated flow through channels. Since channel width is generally small relative to the catchment extent, accurate channel representation requires fine domain discretization, thereby increasing computational overhead. This study aims to develop a computationally efficient hybrid coupled 1D-2D framework with module-specific time-stepping for channel and overland flows, based on various forms of depth-averaged conservation laws, selected in accordance with their physical applicability. Overland flow is modeled using the 2D dynamic and diffusive variants of the shallow water equations, and the 1D dynamic (width-averaged, hyperbolic) counterpart governs the flow through channel(s). Bends/junctions formed by channel network involve changes in flow direction and are resolved locally as a 2D system. All the modules are duly coupled at the shared boundary between 1D and 2D systems through interfacial fluxes. The governing partial differential equations are solved on a regular finite-volume grid using an explicit shock-capturing scheme for the dynamic variants, whereas the diffusive model is solved with an implicit temporal discretization. The numerical framework incorporates appropriate treatment of bed variation, wet–dry transitions, and friction to ensure physically admissible solutions. The proposed framework is validated against multiple benchmark scenarios, including experimental cases involving variable-width-channel, channel-networks, and overland-flow (with/without channel) scenarios as well as an extension to real catchments with varying topographical features. The results demonstrate that the dynamic variant better captures rapidly varying and inertia-dominated flows, while the diffusive variant provides computational advantages for gradually varying shallow overland flow.