Mesh, Hydrodynamic Boundary, and Uncertainty Analysis of the 2D‐SWEs: Taking Numerical Simulation of River Networks as an Example

Abstract Targeting the issues of insufficient predictive ability and inefficient computation in two‐dimensional shallow water equations (2D‐SWEs), this study deeply couples the mesh and hydrodynamic boundary, constructing multiple 2D hydrodynamic models (run 2,640 times). This study proposes and validates, for the first time, a hydrodynamic boundary classification framework (strongly and weakly constrained boundary) based on constraint strength, and systematically quantifies the uncertainty and computational performance of various meshes under different boundaries. Two reasons for insufficient predictive ability were identified: improper boundary setting and mesh selection. Through numerical analysis and theoretical derivation, it was demonstrated that appropriate boundary and mesh choices can reduce the uncertainty of 2D‐SWEs. Calculation results indicate that the strongly constrained boundary (water level) significantly reduces model errors; the Unstructured Quadrilateral Mesh (UQM) demonstrates excellent computational robustness, with cumulative deviations in simulated water levels reduced by 30 ∼ 90% compared to the Unstructured Triangular Mesh (UTM). Additionally, the impact of hydrodynamic boundary types on computational efficiency varies with changes in mesh density, type, topography, and other parameters, but the impact of boundary type on computational efficiency does not exceed 4%. UQM improves computational efficiency by 55% ∼ 130% compared to UTM. Additionally, this study identifies the “impossible triangle” region in quadrilateral meshes, which constrains the generation of high‐quality meshes. Taking into account the different grid computational performance, flux propagation characteristics, grid quality, and the convenience of large‐scale applications, it is recommended to primarily use UQM in river channels and UTM in floodplains.